!-------------------------------------------------------------------------------------------------- !> @author Denny Tjahjanto, Max-Planck-Institut für Eisenforschung GmbH !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @brief Relaxed grain cluster (RGC) homogenization scheme !> Ngrains is defined as p x q x r (cluster) !-------------------------------------------------------------------------------------------------- module homogenization_RGC use prec, only: & pReal, & pInt implicit none private integer(pInt), dimension(:), allocatable, public :: & homogenization_RGC_sizeState, & homogenization_RGC_sizePostResults integer(pInt), dimension(:,:), allocatable,target, public :: & homogenization_RGC_sizePostResult character(len=64), dimension(:,:), allocatable,target, public :: & homogenization_RGC_output ! name of each post result output integer(pInt), dimension(:), allocatable,target, public :: & homogenization_RGC_Noutput !< number of outputs per homog instance integer(pInt), dimension(:,:), allocatable, private :: & homogenization_RGC_Ngrains real(pReal), dimension(:,:), allocatable, private :: & homogenization_RGC_dAlpha, & homogenization_RGC_angles real(pReal), dimension(:,:,:,:), allocatable, private :: & homogenization_RGC_orientation real(pReal), dimension(:), allocatable, private :: & homogenization_RGC_xiAlpha, & homogenization_RGC_ciAlpha enum, bind(c) enumerator :: undefined_ID, & constitutivework_ID, & penaltyenergy_ID, & volumediscrepancy_ID, & averagerelaxrate_ID,& maximumrelaxrate_ID,& ipcoords_ID,& magnitudemismatch_ID,& avgdefgrad_ID,& avgfirstpiola_ID end enum integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: & homogenization_RGC_outputID !< ID of each post result output public :: & homogenization_RGC_init, & homogenization_RGC_partitionDeformation, & homogenization_RGC_averageStressAndItsTangent, & homogenization_RGC_updateState, & homogenization_RGC_postResults private :: & homogenization_RGC_stressPenalty, & homogenization_RGC_volumePenalty, & homogenization_RGC_grainDeformation, & homogenization_RGC_surfaceCorrection, & homogenization_RGC_equivalentModuli, & homogenization_RGC_relaxationVector, & homogenization_RGC_interfaceNormal, & homogenization_RGC_getInterface, & homogenization_RGC_grain1to3, & homogenization_RGC_grain3to1, & homogenization_RGC_interface4to1, & homogenization_RGC_interface1to4 contains !-------------------------------------------------------------------------------------------------- !> @brief allocates all neccessary fields, reads information from material configuration file !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_init(fileUnit) use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use prec, only: & pReal, & pInt use debug, only: & debug_level, & debug_homogenization, & debug_levelBasic, & debug_levelExtensive use math, only: & math_Mandel3333to66,& math_Voigt66to3333, & math_I3, & math_sampleRandomOri,& math_EulerToR,& INRAD use mesh, only: & mesh_maxNips, & mesh_NcpElems,& mesh_element, & FE_Nips, & FE_geomtype use IO use material use numerics, only: & worldrank implicit none integer(pInt), intent(in) :: fileUnit !< file pointer to material configuration integer(pInt), allocatable, dimension(:) :: chunkPos integer :: & homog, & NofMyHomog, & o, & instance, & sizeHState integer(pInt) :: section=0_pInt, maxNinstance, i,j,e, mySize, myInstance character(len=65536) :: & tag = '', & line = '' mainProcess: if (worldrank == 0) then write(6,'(/,a)') ' <<<+- homogenization_'//HOMOGENIZATION_RGC_label//' init -+>>>' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" endif mainProcess maxNinstance = int(count(homogenization_type == HOMOGENIZATION_RGC_ID),pInt) if (maxNinstance == 0_pInt) return if (iand(debug_level(debug_HOMOGENIZATION),debug_levelBasic) /= 0_pInt) & write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance allocate(homogenization_RGC_sizeState(maxNinstance), source=0_pInt) allocate(homogenization_RGC_sizePostResults(maxNinstance), source=0_pInt) allocate(homogenization_RGC_Noutput(maxNinstance), source=0_pInt) allocate(homogenization_RGC_Ngrains(3,maxNinstance), source=0_pInt) allocate(homogenization_RGC_ciAlpha(maxNinstance), source=0.0_pReal) allocate(homogenization_RGC_xiAlpha(maxNinstance), source=0.0_pReal) allocate(homogenization_RGC_dAlpha(3,maxNinstance), source=0.0_pReal) allocate(homogenization_RGC_angles(3,maxNinstance), source=400.0_pReal) allocate(homogenization_RGC_output(maxval(homogenization_Noutput),maxNinstance)) homogenization_RGC_output='' allocate(homogenization_RGC_outputID(maxval(homogenization_Noutput),maxNinstance),source=undefined_ID) allocate(homogenization_RGC_sizePostResult(maxval(homogenization_Noutput),maxNinstance),& source=0_pInt) allocate(homogenization_RGC_orientation(3,3,mesh_maxNips,mesh_NcpElems), source=0.0_pReal) homogenization_RGC_orientation = spread(spread(math_I3,3,mesh_maxNips),4,mesh_NcpElems) ! initialize to identity rewind(fileUnit) do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>'))/=material_partHomogenization) ! wind forward to line = IO_read(fileUnit) enddo parsingFile: do while (trim(line) /= IO_EOF) ! read through sections of homogenization part line = IO_read(fileUnit) if (IO_isBlank(line)) cycle ! skip empty lines if (IO_getTag(line,'<','>') /= '') then ! stop at next part line = IO_read(fileUnit, .true.) ! reset IO_read exit endif if (IO_getTag(line,'[',']') /= '') then ! next section section = section + 1_pInt cycle endif if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if-statement). It's not safe in Fortran if (homogenization_type(section) == HOMOGENIZATION_RGC_ID) then ! one of my sections i = homogenization_typeInstance(section) ! which instance of my type is present homogenization chunkPos = IO_stringPos(line) tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key select case(tag) case ('(output)') select case(IO_lc(IO_stringValue(line,chunkPos,2_pInt))) case('constitutivework') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = constitutivework_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('penaltyenergy') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = penaltyenergy_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('volumediscrepancy') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = volumediscrepancy_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('averagerelaxrate') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = averagerelaxrate_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('maximumrelaxrate') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = maximumrelaxrate_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('magnitudemismatch') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = magnitudemismatch_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('ipcoords') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = ipcoords_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('avgdefgrad','avgf') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = avgdefgrad_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) case('avgp','avgfirstpiola','avg1stpiola') homogenization_RGC_Noutput(i) = homogenization_RGC_Noutput(i) + 1_pInt homogenization_RGC_outputID(homogenization_RGC_Noutput(i),i) = avgfirstpiola_ID homogenization_RGC_output(homogenization_RGC_Noutput(i),i) = & IO_lc(IO_stringValue(line,chunkPos,2_pInt)) end select case ('clustersize') homogenization_RGC_Ngrains(1,i) = IO_intValue(line,chunkPos,2_pInt) homogenization_RGC_Ngrains(2,i) = IO_intValue(line,chunkPos,3_pInt) homogenization_RGC_Ngrains(3,i) = IO_intValue(line,chunkPos,4_pInt) if (homogenization_Ngrains(section) /= product(homogenization_RGC_Ngrains(1:3,i))) & call IO_error(211_pInt,ext_msg=trim(tag)//' ('//HOMOGENIZATION_RGC_label//')') case ('scalingparameter') homogenization_RGC_xiAlpha(i) = IO_floatValue(line,chunkPos,2_pInt) case ('overproportionality') homogenization_RGC_ciAlpha(i) = IO_floatValue(line,chunkPos,2_pInt) case ('grainsize') homogenization_RGC_dAlpha(1,i) = IO_floatValue(line,chunkPos,2_pInt) homogenization_RGC_dAlpha(2,i) = IO_floatValue(line,chunkPos,3_pInt) homogenization_RGC_dAlpha(3,i) = IO_floatValue(line,chunkPos,4_pInt) case ('clusterorientation') homogenization_RGC_angles(1,i) = IO_floatValue(line,chunkPos,2_pInt) homogenization_RGC_angles(2,i) = IO_floatValue(line,chunkPos,3_pInt) homogenization_RGC_angles(3,i) = IO_floatValue(line,chunkPos,4_pInt) end select endif endif enddo parsingFile !-------------------------------------------------------------------------------------------------- ! * assigning cluster orientations elementLooping: do e = 1_pInt,mesh_NcpElems if (homogenization_type(mesh_element(3,e)) == HOMOGENIZATION_RGC_ID) then myInstance = homogenization_typeInstance(mesh_element(3,e)) if (all (homogenization_RGC_angles(1:3,myInstance) >= 399.9_pReal)) then homogenization_RGC_orientation(1:3,1:3,1,e) = math_EulerToR(math_sampleRandomOri()) do i = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,e))) if (microstructure_elemhomo(mesh_element(4,e))) then homogenization_RGC_orientation(1:3,1:3,i,e) = homogenization_RGC_orientation(1:3,1:3,1,e) else homogenization_RGC_orientation(1:3,1:3,i,e) = math_EulerToR(math_sampleRandomOri()) endif enddo else do i = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,e))) homogenization_RGC_orientation(1:3,1:3,i,e) = & math_EulerToR(homogenization_RGC_angles(1:3,myInstance)*inRad) enddo endif endif enddo elementLooping if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then do i = 1_pInt,maxNinstance write(6,'(a15,1x,i4,/)') 'instance: ', i write(6,'(a25,3(1x,i8))') 'cluster size: ',(homogenization_RGC_Ngrains(j,i),j=1_pInt,3_pInt) write(6,'(a25,1x,e10.3)') 'scaling parameter: ', homogenization_RGC_xiAlpha(i) write(6,'(a25,1x,e10.3)') 'over-proportionality: ', homogenization_RGC_ciAlpha(i) write(6,'(a25,3(1x,e10.3))') 'grain size: ',(homogenization_RGC_dAlpha(j,i),j=1_pInt,3_pInt) write(6,'(a25,3(1x,e10.3))') 'cluster orientation: ',(homogenization_RGC_angles(j,i),j=1_pInt,3_pInt) enddo endif !-------------------------------------------------------------------------------------------------- initializeInstances: do homog = 1_pInt, material_Nhomogenization myHomog: if (homogenization_type(homog) == HOMOGENIZATION_RGC_ID) then NofMyHomog = count(material_homog == homog) instance = homogenization_typeInstance(homog) ! * Determine size of postResults array outputsLoop: do o = 1_pInt, homogenization_RGC_Noutput(instance) select case(homogenization_RGC_outputID(o,instance)) case(constitutivework_ID,penaltyenergy_ID,volumediscrepancy_ID, & averagerelaxrate_ID,maximumrelaxrate_ID) mySize = 1_pInt case(ipcoords_ID,magnitudemismatch_ID) mySize = 3_pInt case(avgdefgrad_ID,avgfirstpiola_ID) mySize = 9_pInt case default mySize = 0_pInt end select outputFound: if (mySize > 0_pInt) then homogenization_RGC_sizePostResult(o,instance) = mySize homogenization_RGC_sizePostResults(instance) = & homogenization_RGC_sizePostResults(instance) + mySize endif outputFound enddo outputsLoop sizeHState = & 3_pInt*(homogenization_RGC_Ngrains(1,instance)-1_pInt)* & homogenization_RGC_Ngrains(2,instance)*homogenization_RGC_Ngrains(3,instance) & + 3_pInt*homogenization_RGC_Ngrains(1,instance)*(homogenization_RGC_Ngrains(2,instance)-1_pInt)* & homogenization_RGC_Ngrains(3,instance) & + 3_pInt*homogenization_RGC_Ngrains(1,instance)*homogenization_RGC_Ngrains(2,instance)* & (homogenization_RGC_Ngrains(3,instance)-1_pInt) & + 8_pInt ! (1) Average constitutive work, (2-4) Overall mismatch, (5) Average penalty energy, ! (6) Volume discrepancy, (7) Avg relaxation rate component, (8) Max relaxation rate component ! allocate state arrays homogState(homog)%sizeState = sizeHState homogState(homog)%sizePostResults = homogenization_RGC_sizePostResults(instance) allocate(homogState(homog)%state0 (sizeHState,NofMyHomog), source=0.0_pReal) allocate(homogState(homog)%subState0(sizeHState,NofMyHomog), source=0.0_pReal) allocate(homogState(homog)%state (sizeHState,NofMyHomog), source=0.0_pReal) endif myHomog enddo initializeInstances end subroutine homogenization_RGC_init !-------------------------------------------------------------------------------------------------- !> @brief partitions the deformation gradient onto the constituents !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_partitionDeformation(F,avgF,ip,el) use debug, only: & debug_level, & debug_homogenization, & debug_levelExtensive use mesh, only: & mesh_element use material, only: & homogenization_maxNgrains, & homogenization_Ngrains,& homogenization_typeInstance implicit none real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F !< partioned F per grain real(pReal), dimension (3,3), intent(in) :: avgF !< averaged F integer(pInt), intent(in) :: & ip, & !< integration point number el !< element number real(pReal), dimension (3) :: aVect,nVect integer(pInt), dimension (4) :: intFace integer(pInt), dimension (3) :: iGrain3 integer(pInt) :: homID, iGrain,iFace,i,j integer(pInt), parameter :: nFace = 6_pInt !-------------------------------------------------------------------------------------------------- ! compute the deformation gradient of individual grains due to relaxations homID = homogenization_typeInstance(mesh_element(3,el)) F = 0.0_pReal do iGrain = 1_pInt,homogenization_Ngrains(mesh_element(3,el)) iGrain3 = homogenization_RGC_grain1to3(iGrain,homID) do iFace = 1_pInt,nFace intFace = homogenization_RGC_getInterface(iFace,iGrain3) ! identifying 6 interfaces of each grain aVect = homogenization_RGC_relaxationVector(intFace,homID, ip, el) ! get the relaxation vectors for each interface from global relaxation vector array nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the normal of each interface forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) & F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! calculating deformation relaxations due to interface relaxation enddo F(1:3,1:3,iGrain) = F(1:3,1:3,iGrain) + avgF ! resulting relaxed deformation gradient !-------------------------------------------------------------------------------------------------- ! debugging the grain deformation gradients if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a32,1x,i3)')'Deformation gradient of grain: ',iGrain do i = 1_pInt,3_pInt write(6,'(1x,3(e15.8,1x))')(F(i,j,iGrain), j = 1_pInt,3_pInt) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif enddo end subroutine homogenization_RGC_partitionDeformation !-------------------------------------------------------------------------------------------------- !> @brief update the internal state of the homogenization scheme and tell whether "done" and ! "happy" with result !-------------------------------------------------------------------------------------------------- function homogenization_RGC_updateState(P,F,F0,avgF,dt,dPdF,ip,el) use prec, only: & dEq use debug, only: & debug_level, & debug_homogenization,& debug_levelExtensive, & debug_e, & debug_i use math, only: & math_invert use mesh, only: & mesh_element use material, only: & homogenization_maxNgrains, & homogenization_typeInstance, & homogState, & mappingHomogenization, & homogenization_Ngrains use numerics, only: & absTol_RGC, & relTol_RGC, & absMax_RGC, & relMax_RGC, & pPert_RGC, & maxdRelax_RGC, & viscPower_RGC, & viscModus_RGC, & refRelaxRate_RGC implicit none real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: & P,& !< array of P F,& !< array of F F0 !< array of initial F real(pReal), dimension (3,3,3,3,homogenization_maxNgrains), intent(in) :: dPdF !< array of current grain stiffness real(pReal), dimension (3,3), intent(in) :: avgF !< average F real(pReal), intent(in) :: dt !< time increment integer(pInt), intent(in) :: & ip, & !< integration point number el !< element number logical, dimension(2) :: homogenization_RGC_updateState integer(pInt), dimension (4) :: intFaceN,intFaceP,faceID integer(pInt), dimension (3) :: nGDim,iGr3N,iGr3P,stresLoc integer(pInt), dimension (2) :: residLoc integer(pInt) homID,iNum,i,j,nIntFaceTot,iGrN,iGrP,iMun,iFace,k,l,ipert,iGrain,nGrain real(pReal), dimension (3,3,homogenization_maxNgrains) :: R,pF,pR,D,pD real(pReal), dimension (3,homogenization_maxNgrains) :: NN,pNN real(pReal), dimension (3) :: normP,normN,mornP,mornN real(pReal) :: residMax,stresMax,constitutiveWork,penaltyEnergy,volDiscrep logical error integer(pInt), parameter :: nFace = 6_pInt real(pReal), dimension(:,:), allocatable :: tract,jmatrix,jnverse,smatrix,pmatrix,rmatrix real(pReal), dimension(:), allocatable :: resid,relax,p_relax,p_resid,drelax zeroTimeStep: if(dEq(dt,0.0_pReal)) then homogenization_RGC_updateState = .true. ! pretend everything is fine and return return endif zeroTimeStep !-------------------------------------------------------------------------------------------------- ! get the dimension of the cluster (grains and interfaces) homID = homogenization_typeInstance(mesh_element(3,el)) nGDim = homogenization_RGC_Ngrains(1:3,homID) nGrain = homogenization_Ngrains(mesh_element(3,el)) nIntFaceTot = (nGDim(1)-1_pInt)*nGDim(2)*nGDim(3) + nGDim(1)*(nGDim(2)-1_pInt)*nGDim(3) & + nGDim(1)*nGDim(2)*(nGDim(3)-1_pInt) !-------------------------------------------------------------------------------------------------- ! allocate the size of the global relaxation arrays/jacobian matrices depending on the size of the cluster allocate(resid(3_pInt*nIntFaceTot), source=0.0_pReal) allocate(tract(nIntFaceTot,3), source=0.0_pReal) allocate(relax(3_pInt*nIntFaceTot)); relax= homogState(mappingHomogenization(2,ip,el))% & state(1:3_pInt*nIntFaceTot,mappingHomogenization(1,ip,el)) allocate(drelax(3_pInt*nIntFaceTot)); drelax= homogState(mappingHomogenization(2,ip,el))% & state(1:3_pInt*nIntFaceTot,mappingHomogenization(1,ip,el)) - & homogState(mappingHomogenization(2,ip,el))% & state0(1:3_pInt*nIntFaceTot,mappingHomogenization(1,ip,el)) !-------------------------------------------------------------------------------------------------- ! debugging the obtained state if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Obtained state: ' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,2(e15.8,1x))')homogState(mappingHomogenization(2,ip,el))%state(i,mappingHomogenization(1,ip,el)) enddo write(6,*)' ' !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! computing interface mismatch and stress penalty tensor for all interfaces of all grains call homogenization_RGC_stressPenalty(R,NN,avgF,F,ip,el,homID) !-------------------------------------------------------------------------------------------------- ! calculating volume discrepancy and stress penalty related to overall volume discrepancy call homogenization_RGC_volumePenalty(D,volDiscrep,F,avgF,ip,el) !-------------------------------------------------------------------------------------------------- ! debugging the mismatch, stress and penalties of grains if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) do iGrain = 1_pInt,nGrain write(6,'(1x,a30,1x,i3,1x,a4,3(1x,e15.8))')'Mismatch magnitude of grain(',iGrain,') :',& NN(1,iGrain),NN(2,iGrain),NN(3,iGrain) write(6,'(/,1x,a30,1x,i3)')'Stress and penalties of grain: ',iGrain do i = 1_pInt,3_pInt write(6,'(1x,3(e15.8,1x),1x,3(e15.8,1x),1x,3(e15.8,1x))')(P(i,j,iGrain), j = 1_pInt,3_pInt), & (R(i,j,iGrain), j = 1_pInt,3_pInt), & (D(i,j,iGrain), j = 1_pInt,3_pInt) enddo write(6,*)' ' enddo !$OMP END CRITICAL (write2out) endif !------------------------------------------------------------------------------------------------ ! computing the residual stress from the balance of traction at all (interior) interfaces do iNum = 1_pInt,nIntFaceTot faceID = homogenization_RGC_interface1to4(iNum,homID) ! identifying the interface ID in local coordinate system (4-dimensional index) !-------------------------------------------------------------------------------------------------- ! identify the left/bottom/back grain (-|N) iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate system (3-dimensional index) iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate the local grain ID into global coordinate system (1-dimensional index) intFaceN = homogenization_RGC_getInterface(2_pInt*faceID(1),iGr3N) normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the interface normal !-------------------------------------------------------------------------------------------------- ! identify the right/up/front grain (+|P) iGr3P = iGr3N iGr3P(faceID(1)) = iGr3N(faceID(1))+1_pInt ! identifying the grain ID in local coordinate system (3-dimensional index) iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate the local grain ID into global coordinate system (1-dimensional index) intFaceP = homogenization_RGC_getInterface(2_pInt*faceID(1)-1_pInt,iGr3P) normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the interface normal !-------------------------------------------------------------------------------------------------- ! compute the residual of traction at the interface (in local system, 4-dimensional index) do i = 1_pInt,3_pInt tract(iNum,i) = sign(viscModus_RGC*(abs(drelax(i+3*(iNum-1_pInt)))/(refRelaxRate_RGC*dt))**viscPower_RGC, & drelax(i+3*(iNum-1_pInt))) ! contribution from the relaxation viscosity do j = 1_pInt,3_pInt tract(iNum,i) = tract(iNum,i) + (P(i,j,iGrP) + R(i,j,iGrP) + D(i,j,iGrP))*normP(j) & ! contribution from material stress P, mismatch penalty R, and volume penalty D projected into the interface + (P(i,j,iGrN) + R(i,j,iGrN) + D(i,j,iGrN))*normN(j) resid(i+3_pInt*(iNum-1_pInt)) = tract(iNum,i) ! translate the local residual into global 1-dimensional residual array enddo enddo !-------------------------------------------------------------------------------------------------- ! debugging the residual stress if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30,1x,i3)')'Traction at interface: ',iNum write(6,'(1x,3(e15.8,1x))')(tract(iNum,j), j = 1_pInt,3_pInt) write(6,*)' ' !$OMP END CRITICAL (write2out) endif enddo !-------------------------------------------------------------------------------------------------- ! convergence check for stress residual stresMax = maxval(abs(P)) ! get the maximum of first Piola-Kirchhoff (material) stress stresLoc = int(maxloc(abs(P)),pInt) ! get the location of the maximum stress residMax = maxval(abs(tract)) ! get the maximum of the residual residLoc = int(maxloc(abs(tract)),pInt) ! get the position of the maximum residual !-------------------------------------------------------------------------------------------------- ! Debugging the convergent criteria if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a)')' ' write(6,'(1x,a,1x,i2,1x,i4)')'RGC residual check ...',ip,el write(6,'(1x,a15,1x,e15.8,1x,a7,i3,1x,a12,i2,i2)')'Max stress: ',stresMax, & '@ grain',stresLoc(3),'in component',stresLoc(1),stresLoc(2) write(6,'(1x,a15,1x,e15.8,1x,a7,i3,1x,a12,i2)')'Max residual: ',residMax, & '@ iface',residLoc(1),'in direction',residLoc(2) flush(6) !$OMP END CRITICAL (write2out) endif homogenization_RGC_updateState = .false. !-------------------------------------------------------------------------------------------------- ! If convergence reached => done and happy if (residMax < relTol_RGC*stresMax .or. residMax < absTol_RGC) then homogenization_RGC_updateState = .true. if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a55,/)')'... done and happy' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! compute/update the state for postResult, i.e., all energy densities computed by time-integration constitutiveWork = homogState(mappingHomogenization(2,ip,el))%state(3*nIntFaceTot+1,mappingHomogenization(1,ip,el)) penaltyEnergy = homogState(mappingHomogenization(2,ip,el))%state(3*nIntFaceTot+5,mappingHomogenization(1,ip,el)) do iGrain = 1_pInt,homogenization_Ngrains(mesh_element(3,el)) ! time-integration loop for the calculating the work and energy do i = 1_pInt,3_pInt do j = 1_pInt,3_pInt constitutiveWork = constitutiveWork + P(i,j,iGrain)*(F(i,j,iGrain) - F0(i,j,iGrain))/real(nGrain,pReal) penaltyEnergy = penaltyEnergy + R(i,j,iGrain)*(F(i,j,iGrain) - F0(i,j,iGrain))/real(nGrain,pReal) enddo enddo enddo homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+1,mappingHomogenization(1,ip,el)) = constitutiveWork ! the bulk mechanical/constitutive work homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+2,mappingHomogenization(1,ip,el)) = sum(NN(1,:))/real(nGrain,pReal) ! the overall mismatch of all interface normal to e1-direction homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+3,mappingHomogenization(1,ip,el)) = sum(NN(2,:))/real(nGrain,pReal) ! the overall mismatch of all interface normal to e2-direction homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+4,mappingHomogenization(1,ip,el)) = sum(NN(3,:))/real(nGrain,pReal) ! the overall mismatch of all interface normal to e3-direction homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+5,mappingHomogenization(1,ip,el)) = penaltyEnergy ! the overall penalty energy homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+6,mappingHomogenization(1,ip,el)) = volDiscrep ! the overall volume discrepancy homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+7,mappingHomogenization(1,ip,el)) = & sum(abs(drelax))/dt/real(3_pInt*nIntFaceTot,pReal) ! the average rate of relaxation vectors homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+8,mappingHomogenization(1,ip,el)) = maxval(abs(drelax))/dt ! the maximum rate of relaxation vectors if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a30,1x,e15.8)') 'Constitutive work: ',constitutiveWork write(6,'(1x,a30,3(1x,e15.8))')'Magnitude mismatch: ',sum(NN(1,:))/real(nGrain,pReal), & sum(NN(2,:))/real(nGrain,pReal), & sum(NN(3,:))/real(nGrain,pReal) write(6,'(1x,a30,1x,e15.8)') 'Penalty energy: ',penaltyEnergy write(6,'(1x,a30,1x,e15.8,/)') 'Volume discrepancy: ',volDiscrep write(6,'(1x,a30,1x,e15.8)') 'Maximum relaxation rate: ',maxval(abs(drelax))/dt write(6,'(1x,a30,1x,e15.8,/)') 'Average relaxation rate: ',sum(abs(drelax))/dt/real(3_pInt*nIntFaceTot,pReal) flush(6) !$OMP END CRITICAL (write2out) endif deallocate(tract,resid,relax,drelax) return !-------------------------------------------------------------------------------------------------- ! if residual blows-up => done but unhappy elseif (residMax > relMax_RGC*stresMax .or. residMax > absMax_RGC) then ! try to restart when residual blows up exceeding maximum bound homogenization_RGC_updateState = [.true.,.false.] ! with direct cut-back if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a55,/)')'... broken' flush(6) !$OMP END CRITICAL (write2out) endif deallocate(tract,resid,relax,drelax) return else ! proceed with computing the Jacobian and state update if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a55,/)')'... not yet done' flush(6) !$OMP END CRITICAL (write2out) endif endif !--------------------------------------------------------------------------------------------------- ! construct the global Jacobian matrix for updating the global relaxation vector array when ! convergence is not yet reached ... !-------------------------------------------------------------------------------------------------- ! ... of the constitutive stress tangent, assembled from dPdF or material constitutive model "smatrix" allocate(smatrix(3*nIntFaceTot,3*nIntFaceTot), source=0.0_pReal) do iNum = 1_pInt,nIntFaceTot faceID = homogenization_RGC_interface1to4(iNum,homID) ! assembling of local dPdF into global Jacobian matrix !-------------------------------------------------------------------------------------------------- ! identify the left/bottom/back grain (-|N) iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate sytem iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate into global grain ID intFaceN = homogenization_RGC_getInterface(2_pInt*faceID(1),iGr3N) ! identifying the connecting interface in local coordinate system normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the interface normal do iFace = 1_pInt,nFace intFaceN = homogenization_RGC_getInterface(iFace,iGr3N) ! identifying all interfaces that influence relaxation of the above interface mornN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get normal of the interfaces iMun = homogenization_RGC_interface4to1(intFaceN,homID) ! translate the interfaces ID into local 4-dimensional index if (iMun > 0) then ! get the corresponding tangent do i=1_pInt,3_pInt; do j=1_pInt,3_pInt; do k=1_pInt,3_pInt; do l=1_pInt,3_pInt smatrix(3*(iNum-1)+i,3*(iMun-1)+j) = smatrix(3*(iNum-1)+i,3*(iMun-1)+j) + dPdF(i,k,j,l,iGrN)*normN(k)*mornN(l) enddo;enddo;enddo;enddo ! projecting the material tangent dPdF into the interface ! to obtain the Jacobian matrix contribution of dPdF endif enddo !-------------------------------------------------------------------------------------------------- ! identify the right/up/front grain (+|P) iGr3P = iGr3N iGr3P(faceID(1)) = iGr3N(faceID(1))+1_pInt ! identifying the grain ID in local coordinate sytem iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate into global grain ID intFaceP = homogenization_RGC_getInterface(2_pInt*faceID(1)-1_pInt,iGr3P) ! identifying the connecting interface in local coordinate system normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the interface normal do iFace = 1_pInt,nFace intFaceP = homogenization_RGC_getInterface(iFace,iGr3P) ! identifying all interfaces that influence relaxation of the above interface mornP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get normal of the interfaces iMun = homogenization_RGC_interface4to1(intFaceP,homID) ! translate the interfaces ID into local 4-dimensional index if (iMun > 0_pInt) then ! get the corresponding tangent do i=1_pInt,3_pInt; do j=1_pInt,3_pInt; do k=1_pInt,3_pInt; do l=1_pInt,3_pInt smatrix(3*(iNum-1)+i,3*(iMun-1)+j) = smatrix(3*(iNum-1)+i,3*(iMun-1)+j) + dPdF(i,k,j,l,iGrP)*normP(k)*mornP(l) enddo;enddo;enddo;enddo endif enddo enddo !-------------------------------------------------------------------------------------------------- ! debugging the global Jacobian matrix of stress tangent if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Jacobian matrix of stress' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,100(e11.4,1x))')(smatrix(i,j), j = 1_pInt,3_pInt*nIntFaceTot) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! ... of the stress penalty tangent (mismatch penalty and volume penalty, computed using numerical ! perturbation method) "pmatrix" allocate(pmatrix(3*nIntFaceTot,3*nIntFaceTot), source=0.0_pReal) allocate(p_relax(3*nIntFaceTot), source=0.0_pReal) allocate(p_resid(3*nIntFaceTot), source=0.0_pReal) do ipert = 1_pInt,3_pInt*nIntFaceTot p_relax = relax p_relax(ipert) = relax(ipert) + pPert_RGC ! perturb the relaxation vector homogState(mappingHomogenization(2,ip,el))%state(1:3*nIntFaceTot,mappingHomogenization(1,ip,el)) = p_relax call homogenization_RGC_grainDeformation(pF,avgF,ip,el) ! compute the grains deformation from perturbed state call homogenization_RGC_stressPenalty(pR,pNN,avgF,pF,ip,el,homID) ! compute stress penalty due to interface mismatch from perturbed state call homogenization_RGC_volumePenalty(pD,volDiscrep,pF,avgF,ip,el) ! compute stress penalty due to volume discrepancy from perturbed state !-------------------------------------------------------------------------------------------------- ! computing the global stress residual array from the perturbed state p_resid = 0.0_pReal do iNum = 1_pInt,nIntFaceTot faceID = homogenization_RGC_interface1to4(iNum,homID) ! identifying the interface ID in local coordinate system (4-dimensional index) !-------------------------------------------------------------------------------------------------- ! identify the left/bottom/back grain (-|N) iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate system (3-dimensional index) iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate the local grain ID into global coordinate system (1-dimensional index) intFaceN = homogenization_RGC_getInterface(2_pInt*faceID(1),iGr3N) ! identifying the interface ID of the grain normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the corresponding interface normal !-------------------------------------------------------------------------------------------------- ! identify the right/up/front grain (+|P) iGr3P = iGr3N iGr3P(faceID(1)) = iGr3N(faceID(1))+1_pInt ! identifying the grain ID in local coordinate system (3-dimensional index) iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate the local grain ID into global coordinate system (1-dimensional index) intFaceP = homogenization_RGC_getInterface(2_pInt*faceID(1)-1_pInt,iGr3P) ! identifying the interface ID of the grain normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the corresponding normal !-------------------------------------------------------------------------------------------------- ! compute the residual stress (contribution of mismatch and volume penalties) from perturbed state ! at all interfaces do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt p_resid(i+3*(iNum-1)) = p_resid(i+3*(iNum-1)) + (pR(i,j,iGrP) - R(i,j,iGrP))*normP(j) & + (pR(i,j,iGrN) - R(i,j,iGrN))*normN(j) & + (pD(i,j,iGrP) - D(i,j,iGrP))*normP(j) & + (pD(i,j,iGrN) - D(i,j,iGrN))*normN(j) enddo; enddo enddo pmatrix(:,ipert) = p_resid/pPert_RGC enddo !-------------------------------------------------------------------------------------------------- ! debugging the global Jacobian matrix of penalty tangent if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Jacobian matrix of penalty' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,100(e11.4,1x))')(pmatrix(i,j), j = 1_pInt,3_pInt*nIntFaceTot) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! ... of the numerical viscosity traction "rmatrix" allocate(rmatrix(3*nIntFaceTot,3*nIntFaceTot),source=0.0_pReal) forall (i=1_pInt:3_pInt*nIntFaceTot) & rmatrix(i,i) = viscModus_RGC*viscPower_RGC/(refRelaxRate_RGC*dt)* & ! tangent due to numerical viscosity traction appears (abs(drelax(i))/(refRelaxRate_RGC*dt))**(viscPower_RGC - 1.0_pReal) ! only in the main diagonal term !-------------------------------------------------------------------------------------------------- ! debugging the global Jacobian matrix of numerical viscosity tangent if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Jacobian matrix of penalty' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,100(e11.4,1x))')(rmatrix(i,j), j = 1_pInt,3_pInt*nIntFaceTot) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! The overall Jacobian matrix summarizing contributions of smatrix, pmatrix, rmatrix allocate(jmatrix(3*nIntFaceTot,3*nIntFaceTot)); jmatrix = smatrix + pmatrix + rmatrix if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Jacobian matrix (total)' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,100(e11.4,1x))')(jmatrix(i,j), j = 1_pInt,3_pInt*nIntFaceTot) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! computing the update of the state variable (relaxation vectors) using the Jacobian matrix allocate(jnverse(3_pInt*nIntFaceTot,3_pInt*nIntFaceTot),source=0.0_pReal) call math_invert(size(jmatrix,1),jmatrix,jnverse,error) ! Compute the inverse of the overall Jacobian matrix !-------------------------------------------------------------------------------------------------- ! debugging the inverse Jacobian matrix if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Jacobian inverse' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,100(e11.4,1x))')(jnverse(i,j), j = 1_pInt,3_pInt*nIntFaceTot) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! calculate the state update (global relaxation vectors) for the next Newton-Raphson iteration drelax = 0.0_pReal do i = 1_pInt,3_pInt*nIntFaceTot do j = 1_pInt,3_pInt*nIntFaceTot drelax(i) = drelax(i) - jnverse(i,j)*resid(j) ! Calculate the correction for the state variable enddo enddo relax = relax + drelax ! Updateing the state variable for the next iteration homogState(mappingHomogenization(2,ip,el))%state(1:3*nIntFaceTot,mappingHomogenization(1,ip,el)) = relax if (any(abs(drelax) > maxdRelax_RGC)) then ! Forcing cutback when the incremental change of relaxation vector becomes too large homogenization_RGC_updateState = [.true.,.false.] !$OMP CRITICAL (write2out) write(6,'(1x,a,1x,i3,1x,a,1x,i3,1x,a)')'RGC_updateState: ip',ip,'| el',el,'enforces cutback' write(6,'(1x,a,1x,e15.8)')'due to large relaxation change =',maxval(abs(drelax)) flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! debugging the return state if (iand(debug_homogenization, debug_levelExtensive) > 0_pInt) then !$OMP CRITICAL (write2out) write(6,'(1x,a30)')'Returned state: ' do i = 1_pInt,3_pInt*nIntFaceTot write(6,'(1x,2(e15.8,1x))')homogState(mappingHomogenization(2,ip,el))%state(i,mappingHomogenization(1,ip,el)) enddo write(6,*)' ' flush(6) !$OMP END CRITICAL (write2out) endif deallocate(tract,resid,jmatrix,jnverse,relax,drelax,pmatrix,smatrix,p_relax,p_resid) end function homogenization_RGC_updateState !-------------------------------------------------------------------------------------------------- !> @brief derive average stress and stiffness from constituent quantities !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_averageStressAndItsTangent(avgP,dAvgPdAvgF,P,dPdF,el) use debug, only: & debug_level, & debug_homogenization,& debug_levelExtensive use mesh, only: mesh_element use material, only: & homogenization_maxNgrains, & homogenization_Ngrains, & homogenization_typeInstance use math, only: math_Plain3333to99 implicit none real(pReal), dimension (3,3), intent(out) :: avgP !< average stress at material point real(pReal), dimension (3,3,3,3), intent(out) :: dAvgPdAvgF !< average stiffness at material point real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: P !< array of current grain stresses real(pReal), dimension (3,3,3,3,homogenization_maxNgrains), intent(in) :: dPdF !< array of current grain stiffnesses integer(pInt), intent(in) :: el !< element number real(pReal), dimension (9,9) :: dPdF99 integer(pInt) :: homID, i, j, Ngrains, iGrain homID = homogenization_typeInstance(mesh_element(3,el)) Ngrains = homogenization_Ngrains(mesh_element(3,el)) !-------------------------------------------------------------------------------------------------- ! debugging the grain tangent if (iand(debug_level(debug_homogenization), debug_levelExtensive) /= 0_pInt) then !$OMP CRITICAL (write2out) do iGrain = 1_pInt,Ngrains dPdF99 = math_Plain3333to99(dPdF(1:3,1:3,1:3,1:3,iGrain)) write(6,'(1x,a30,1x,i3)')'Stress tangent of grain: ',iGrain do i = 1_pInt,9_pInt write(6,'(1x,(e15.8,1x))') (dPdF99(i,j), j = 1_pInt,9_pInt) enddo write(6,*)' ' enddo flush(6) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! computing the average first Piola-Kirchhoff stress P and the average tangent dPdF avgP = sum(P,3)/real(Ngrains,pReal) dAvgPdAvgF = sum(dPdF,5)/real(Ngrains,pReal) end subroutine homogenization_RGC_averageStressAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief return array of homogenization results for post file inclusion !-------------------------------------------------------------------------------------------------- pure function homogenization_RGC_postResults(ip,el,avgP,avgF) use mesh, only: & mesh_element, & mesh_ipCoordinates use material, only: & homogenization_typeInstance,& homogState, & mappingHomogenization, & homogenization_Noutput implicit none integer(pInt), intent(in) :: & ip, & !< integration point number el !< element number real(pReal), dimension(3,3), intent(in) :: & avgP, & !< average stress at material point avgF !< average deformation gradient at material point integer(pInt) homID,o,c,nIntFaceTot real(pReal), dimension(homogenization_RGC_sizePostResults(homogenization_typeInstance(mesh_element(3,el)))) :: & homogenization_RGC_postResults homID = homogenization_typeInstance(mesh_element(3,el)) nIntFaceTot=(homogenization_RGC_Ngrains(1,homID)-1_pInt)*homogenization_RGC_Ngrains(2,homID)*homogenization_RGC_Ngrains(3,homID)& + homogenization_RGC_Ngrains(1,homID)*(homogenization_RGC_Ngrains(2,homID)-1_pInt)*homogenization_RGC_Ngrains(3,homID)& + homogenization_RGC_Ngrains(1,homID)*homogenization_RGC_Ngrains(2,homID)*(homogenization_RGC_Ngrains(3,homID)-1_pInt) c = 0_pInt homogenization_RGC_postResults = 0.0_pReal do o = 1_pInt,homogenization_Noutput(mesh_element(3,el)) select case(homogenization_RGC_outputID(o,homID)) case (avgdefgrad_ID) homogenization_RGC_postResults(c+1_pInt:c+9_pInt) = reshape(avgF,[9]) c = c + 9_pInt case (avgfirstpiola_ID) homogenization_RGC_postResults(c+1_pInt:c+9_pInt) = reshape(avgP,[9]) c = c + 9_pInt case (ipcoords_ID) homogenization_RGC_postResults(c+1_pInt:c+3_pInt) = mesh_ipCoordinates(1:3,ip,el) ! current ip coordinates c = c + 3_pInt case (constitutivework_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+1,mappingHomogenization(1,ip,el)) c = c + 1_pInt case (magnitudemismatch_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+2,mappingHomogenization(1,ip,el)) homogenization_RGC_postResults(c+2) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+3,mappingHomogenization(1,ip,el)) homogenization_RGC_postResults(c+3) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+4,mappingHomogenization(1,ip,el)) c = c + 3_pInt case (penaltyenergy_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+5,mappingHomogenization(1,ip,el)) c = c + 1_pInt case (volumediscrepancy_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+6,mappingHomogenization(1,ip,el)) c = c + 1_pInt case (averagerelaxrate_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+7,mappingHomogenization(1,ip,el)) c = c + 1_pInt case (maximumrelaxrate_ID) homogenization_RGC_postResults(c+1) = homogState(mappingHomogenization(2,ip,el))% & state(3*nIntFaceTot+8,mappingHomogenization(1,ip,el)) c = c + 1_pInt end select enddo end function homogenization_RGC_postResults !-------------------------------------------------------------------------------------------------- !> @brief calculate stress-like penalty due to deformation mismatch !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_stressPenalty(rPen,nMis,avgF,fDef,ip,el,homID) use debug, only: & debug_level, & debug_homogenization,& debug_levelExtensive, & debug_e, & debug_i use mesh, only: & mesh_element use constitutive, only: & constitutive_homogenizedC use math, only: & math_civita use material, only: & homogenization_maxNgrains,& homogenization_Ngrains use numerics, only: & xSmoo_RGC implicit none real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: rPen !< stress-like penalty real(pReal), dimension (3,homogenization_maxNgrains), intent(out) :: nMis !< total amount of mismatch real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef !< deformation gradients real(pReal), dimension (3,3), intent(in) :: avgF !< initial effective stretch tensor integer(pInt), intent(in) :: ip,el integer(pInt), dimension (4) :: intFace integer(pInt), dimension (3) :: iGrain3,iGNghb3,nGDim real(pReal), dimension (3,3) :: gDef,nDef real(pReal), dimension (3) :: nVect,surfCorr real(pReal), dimension (2) :: Gmoduli integer(pInt) :: homID,iGrain,iGNghb,iFace,i,j,k,l real(pReal) :: muGrain,muGNghb,nDefNorm,bgGrain,bgGNghb integer(pInt), parameter :: nFace = 6_pInt real(pReal), parameter :: nDefToler = 1.0e-10_pReal nGDim = homogenization_RGC_Ngrains(1:3,homID) rPen = 0.0_pReal nMis = 0.0_pReal !-------------------------------------------------------------------------------------------------- ! get the correction factor the modulus of penalty stress representing the evolution of area of ! the interfaces due to deformations surfCorr = homogenization_RGC_surfaceCorrection(avgF,ip,el) !-------------------------------------------------------------------------------------------------- ! debugging the surface correction factor if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a20,2(1x,i3))')'Correction factor: ',ip,el write(6,'(1x,3(e11.4,1x))')(surfCorr(i), i = 1,3) !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! computing the mismatch and penalty stress tensor of all grains do iGrain = 1_pInt,homogenization_Ngrains(mesh_element(3,el)) Gmoduli = homogenization_RGC_equivalentModuli(iGrain,ip,el) muGrain = Gmoduli(1) ! collecting the equivalent shear modulus of grain bgGrain = Gmoduli(2) ! and the lengthh of Burgers vector iGrain3 = homogenization_RGC_grain1to3(iGrain,homID) ! get the grain ID in local 3-dimensional index (x,y,z)-position !* Looping over all six interfaces of each grain do iFace = 1_pInt,nFace intFace = homogenization_RGC_getInterface(iFace,iGrain3) ! get the 4-dimensional index of the interface in local numbering system of the grain nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the interface normal iGNghb3 = iGrain3 ! identify the neighboring grain across the interface iGNghb3(abs(intFace(1))) = iGNghb3(abs(intFace(1))) + int(real(intFace(1),pReal)/real(abs(intFace(1)),pReal),pInt) if (iGNghb3(1) < 1) iGNghb3(1) = nGDim(1) ! with periodicity along e1 direction if (iGNghb3(1) > nGDim(1)) iGNghb3(1) = 1_pInt if (iGNghb3(2) < 1) iGNghb3(2) = nGDim(2) ! with periodicity along e2 direction if (iGNghb3(2) > nGDim(2)) iGNghb3(2) = 1_pInt if (iGNghb3(3) < 1) iGNghb3(3) = nGDim(3) ! with periodicity along e3 direction if (iGNghb3(3) > nGDim(3)) iGNghb3(3) = 1_pInt iGNghb = homogenization_RGC_grain3to1(iGNghb3,homID) ! get the ID of the neighboring grain Gmoduli = homogenization_RGC_equivalentModuli(iGNghb,ip,el) ! collecting the shear modulus and Burgers vector of the neighbor muGNghb = Gmoduli(1) bgGNghb = Gmoduli(2) gDef = 0.5_pReal*(fDef(1:3,1:3,iGNghb) - fDef(1:3,1:3,iGrain)) ! compute the difference/jump in deformation gradeint across the neighbor !-------------------------------------------------------------------------------------------------- ! compute the mismatch tensor of all interfaces nDefNorm = 0.0_pReal nDef = 0.0_pReal do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_civita(j,k,l) ! compute the interface mismatch tensor from the jump of deformation gradient enddo; enddo nDefNorm = nDefNorm + nDef(i,j)*nDef(i,j) ! compute the norm of the mismatch tensor enddo; enddo nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity) nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm ! total amount of mismatch experienced by the grain (at all six interfaces) !-------------------------------------------------------------------------------------------------- ! debuggin the mismatch tensor if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a20,i2,1x,a20,1x,i3)')'Mismatch to face: ',intFace(1),'neighbor grain: ',iGNghb do i = 1,3 write(6,'(1x,3(e11.4,1x))')(nDef(i,j), j = 1,3) enddo write(6,'(1x,a20,e11.4)')'with magnitude: ',nDefNorm !$OMP END CRITICAL (write2out) endif !-------------------------------------------------------------------------------------------------- ! compute the stress penalty of all interfaces do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt rPen(i,j,iGrain) = rPen(i,j,iGrain) + 0.5_pReal*(muGrain*bgGrain + muGNghb*bgGNghb)*homogenization_RGC_xiAlpha(homID) & *surfCorr(abs(intFace(1)))/homogenization_RGC_dAlpha(abs(intFace(1)),homID) & *cosh(homogenization_RGC_ciAlpha(homID)*nDefNorm) & *0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_civita(k,l,j) & *tanh(nDefNorm/xSmoo_RGC) enddo; enddo enddo; enddo enddo !-------------------------------------------------------------------------------------------------- ! debugging the stress-like penalty if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a20,i2)')'Penalty of grain: ',iGrain do i = 1,3 write(6,'(1x,3(e11.4,1x))')(rPen(i,j,iGrain), j = 1,3) enddo !$OMP END CRITICAL (write2out) endif enddo end subroutine homogenization_RGC_stressPenalty !-------------------------------------------------------------------------------------------------- !> @brief calculate stress-like penalty due to volume discrepancy !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_volumePenalty(vPen,vDiscrep,fDef,fAvg,ip,el) use debug, only: & debug_level, & debug_homogenization,& debug_levelExtensive, & debug_e, & debug_i use mesh, only: & mesh_element use math, only: & math_det33, & math_inv33 use material, only: & homogenization_maxNgrains,& homogenization_Ngrains use numerics, only: & maxVolDiscr_RGC,& volDiscrMod_RGC,& volDiscrPow_RGC implicit none real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: vPen ! stress-like penalty due to volume real(pReal), intent(out) :: vDiscrep ! total volume discrepancy real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef ! deformation gradients real(pReal), dimension (3,3), intent(in) :: fAvg ! overall deformation gradient integer(pInt), intent(in) :: ip,& ! integration point el real(pReal), dimension (homogenization_maxNgrains) :: gVol integer(pInt) :: iGrain,nGrain,i,j nGrain = homogenization_Ngrains(mesh_element(3,el)) !-------------------------------------------------------------------------------------------------- ! compute the volumes of grains and of cluster vDiscrep = math_det33(fAvg) ! compute the volume of the cluster do iGrain = 1_pInt,nGrain gVol(iGrain) = math_det33(fDef(1:3,1:3,iGrain)) ! compute the volume of individual grains vDiscrep = vDiscrep - gVol(iGrain)/real(nGrain,pReal) ! calculate the difference/dicrepancy between ! the volume of the cluster and the the total volume of grains enddo !-------------------------------------------------------------------------------------------------- ! calculate the stress and penalty due to volume discrepancy vPen = 0.0_pReal do iGrain = 1_pInt,nGrain vPen(:,:,iGrain) = -1.0_pReal/real(nGrain,pReal)*volDiscrMod_RGC*volDiscrPow_RGC/maxVolDiscr_RGC* & sign((abs(vDiscrep)/maxVolDiscr_RGC)**(volDiscrPow_RGC - 1.0),vDiscrep)* & gVol(iGrain)*transpose(math_inv33(fDef(:,:,iGrain))) !-------------------------------------------------------------------------------------------------- ! debugging the stress-like penalty if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt & .and. debug_e == el .and. debug_i == ip) then !$OMP CRITICAL (write2out) write(6,'(1x,a30,i2)')'Volume penalty of grain: ',iGrain do i = 1,3 write(6,'(1x,3(e11.4,1x))')(vPen(i,j,iGrain), j = 1,3) enddo !$OMP END CRITICAL (write2out) endif enddo end subroutine homogenization_RGC_volumePenalty !-------------------------------------------------------------------------------------------------- !> @brief compute the correction factor accouted for surface evolution (area change) due to ! deformation !-------------------------------------------------------------------------------------------------- function homogenization_RGC_surfaceCorrection(avgF,ip,el) use math, only: & math_invert33, & math_mul33x33 implicit none real(pReal), dimension(3) :: homogenization_RGC_surfaceCorrection real(pReal), dimension(3,3), intent(in) :: avgF !< average F integer(pInt), intent(in) :: ip,& !< integration point number el !< element number real(pReal), dimension(3,3) :: invC,avgC real(pReal), dimension(3) :: nVect real(pReal) :: detF integer(pInt), dimension(4) :: intFace integer(pInt) :: i,j,iBase logical :: error avgC = math_mul33x33(transpose(avgF),avgF) call math_invert33(avgC,invC,detF,error) homogenization_RGC_surfaceCorrection = 0.0_pReal do iBase = 1_pInt,3_pInt intFace = [iBase,1_pInt,1_pInt,1_pInt] nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the normal of the interface do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt homogenization_RGC_surfaceCorrection(iBase) = & ! compute the component of (the inverse of) the stretch in the direction of the normal homogenization_RGC_surfaceCorrection(iBase) + invC(i,j)*nVect(i)*nVect(j) enddo; enddo homogenization_RGC_surfaceCorrection(iBase) = & ! get the surface correction factor (area contraction/enlargement) sqrt(homogenization_RGC_surfaceCorrection(iBase))*detF enddo end function homogenization_RGC_surfaceCorrection !-------------------------------------------------------------------------------------------------- !> @brief compute the equivalent shear and bulk moduli from the elasticity tensor !-------------------------------------------------------------------------------------------------- function homogenization_RGC_equivalentModuli(grainID,ip,el) use constitutive, only: & constitutive_homogenizedC implicit none integer(pInt), intent(in) :: & grainID,& ip, & !< integration point number el !< element number real(pReal), dimension (6,6) :: elasTens real(pReal), dimension(2) :: homogenization_RGC_equivalentModuli real(pReal) :: & cEquiv_11, & cEquiv_12, & cEquiv_44 elasTens = constitutive_homogenizedC(grainID,ip,el) !-------------------------------------------------------------------------------------------------- ! compute the equivalent shear modulus after Turterltaub and Suiker, JMPS (2005) cEquiv_11 = (elasTens(1,1) + elasTens(2,2) + elasTens(3,3))/3.0_pReal cEquiv_12 = (elasTens(1,2) + elasTens(2,3) + elasTens(3,1) + & elasTens(1,3) + elasTens(2,1) + elasTens(3,2))/6.0_pReal cEquiv_44 = (elasTens(4,4) + elasTens(5,5) + elasTens(6,6))/3.0_pReal homogenization_RGC_equivalentModuli(1) = 0.2_pReal*(cEquiv_11 - cEquiv_12) + 0.6_pReal*cEquiv_44 !-------------------------------------------------------------------------------------------------- ! obtain the length of Burgers vector (could be model dependend) homogenization_RGC_equivalentModuli(2) = 2.5e-10_pReal end function homogenization_RGC_equivalentModuli !-------------------------------------------------------------------------------------------------- !> @brief collect relaxation vectors of an interface !-------------------------------------------------------------------------------------------------- function homogenization_RGC_relaxationVector(intFace,homID, ip, el) use material, only: & homogState, & mappingHomogenization implicit none integer(pInt), intent(in) :: ip, el real(pReal), dimension (3) :: homogenization_RGC_relaxationVector integer(pInt), dimension (4), intent(in) :: intFace !< set of interface ID in 4D array (normal and position) integer(pInt), dimension (3) :: nGDim integer(pInt) :: & iNum, & homID !< homogenization ID !-------------------------------------------------------------------------------------------------- ! collect the interface relaxation vector from the global state array homogenization_RGC_relaxationVector = 0.0_pReal nGDim = homogenization_RGC_Ngrains(1:3,homID) iNum = homogenization_RGC_interface4to1(intFace,homID) ! identify the position of the interface in global state array if (iNum > 0_pInt) homogenization_RGC_relaxationVector = homogState(mappingHomogenization(2,ip,el))% & state((3*iNum-2):(3*iNum),mappingHomogenization(1,ip,el)) ! get the corresponding entries end function homogenization_RGC_relaxationVector !-------------------------------------------------------------------------------------------------- !> @brief identify the normal of an interface !-------------------------------------------------------------------------------------------------- function homogenization_RGC_interfaceNormal(intFace,ip,el) use debug, only: & debug_homogenization,& debug_levelExtensive use math, only: & math_mul33x3 implicit none real(pReal), dimension (3) :: homogenization_RGC_interfaceNormal integer(pInt), dimension (4), intent(in) :: intFace !< interface ID in 4D array (normal and position) integer(pInt), intent(in) :: & ip, & !< integration point number el !< element number integer(pInt) :: nPos !-------------------------------------------------------------------------------------------------- ! get the normal of the interface, identified from the value of intFace(1) homogenization_RGC_interfaceNormal = 0.0_pReal nPos = abs(intFace(1)) ! identify the position of the interface in global state array homogenization_RGC_interfaceNormal(nPos) = real(intFace(1)/abs(intFace(1)),pReal) ! get the normal vector w.r.t. cluster axis homogenization_RGC_interfaceNormal = & math_mul33x3(homogenization_RGC_orientation(1:3,1:3,ip,el),homogenization_RGC_interfaceNormal) ! map the normal vector into sample coordinate system (basis) end function homogenization_RGC_interfaceNormal !-------------------------------------------------------------------------------------------------- !> @brief collect six faces of a grain in 4D (normal and position) !-------------------------------------------------------------------------------------------------- function homogenization_RGC_getInterface(iFace,iGrain3) implicit none integer(pInt), dimension (4) :: homogenization_RGC_getInterface integer(pInt), dimension (3), intent(in) :: iGrain3 !< grain ID in 3D array integer(pInt), intent(in) :: iFace !< face index (1..6) mapped like (-e1,-e2,-e3,+e1,+e2,+e3) or iDir = (-1,-2,-3,1,2,3) integer(pInt) :: iDir !* Direction of interface normal iDir = (int(real(iFace-1_pInt,pReal)/2.0_pReal,pInt)+1_pInt)*(-1_pInt)**iFace homogenization_RGC_getInterface(1) = iDir !-------------------------------------------------------------------------------------------------- ! identify the interface position by the direction of its normal homogenization_RGC_getInterface(2:4) = iGrain3 if (iDir < 0_pInt) & ! to have a correlation with coordinate/position in real space homogenization_RGC_getInterface(1_pInt-iDir) = homogenization_RGC_getInterface(1_pInt-iDir)-1_pInt end function homogenization_RGC_getInterface !-------------------------------------------------------------------------------------------------- !> @brief map grain ID from in 1D (global array) to in 3D (local position) !-------------------------------------------------------------------------------------------------- function homogenization_RGC_grain1to3(grain1,homID) implicit none integer(pInt), dimension (3) :: homogenization_RGC_grain1to3 integer(pInt), intent(in) :: & grain1,& !< grain ID in 1D array homID !< homogenization ID integer(pInt), dimension (3) :: nGDim !-------------------------------------------------------------------------------------------------- ! get the grain position nGDim = homogenization_RGC_Ngrains(1:3,homID) homogenization_RGC_grain1to3(3) = 1_pInt+(grain1-1_pInt)/(nGDim(1)*nGDim(2)) homogenization_RGC_grain1to3(2) = 1_pInt+mod((grain1-1_pInt)/nGDim(1),nGDim(2)) homogenization_RGC_grain1to3(1) = 1_pInt+mod((grain1-1_pInt),nGDim(1)) end function homogenization_RGC_grain1to3 !-------------------------------------------------------------------------------------------------- !> @brief map grain ID from in 3D (local position) to in 1D (global array) !-------------------------------------------------------------------------------------------------- pure function homogenization_RGC_grain3to1(grain3,homID) implicit none integer(pInt), dimension (3), intent(in) :: grain3 !< grain ID in 3D array (pos.x,pos.y,pos.z) integer(pInt) :: homogenization_RGC_grain3to1 integer(pInt), dimension (3) :: nGDim integer(pInt), intent(in) :: homID ! homogenization ID !-------------------------------------------------------------------------------------------------- ! get the grain ID nGDim = homogenization_RGC_Ngrains(1:3,homID) homogenization_RGC_grain3to1 = grain3(1) + nGDim(1)*(grain3(2)-1_pInt) + nGDim(1)*nGDim(2)*(grain3(3)-1_pInt) end function homogenization_RGC_grain3to1 !-------------------------------------------------------------------------------------------------- !> @brief maps interface ID from 4D (normal and local position) into 1D (global array) !-------------------------------------------------------------------------------------------------- integer(pInt) pure function homogenization_RGC_interface4to1(iFace4D, homID) implicit none integer(pInt), dimension (4), intent(in) :: iFace4D !< interface ID in 4D array (n.dir,pos.x,pos.y,pos.z) integer(pInt), dimension (3) :: nGDim,nIntFace integer(pInt), intent(in) :: homID !< homogenization ID nGDim = homogenization_RGC_Ngrains(1:3,homID) !-------------------------------------------------------------------------------------------------- ! compute the total number of interfaces, which ... nIntFace(1) = (nGDim(1)-1_pInt)*nGDim(2)*nGDim(3) ! ... normal //e1 nIntFace(2) = nGDim(1)*(nGDim(2)-1_pInt)*nGDim(3) ! ... normal //e2 nIntFace(3) = nGDim(1)*nGDim(2)*(nGDim(3)-1_pInt) ! ... normal //e3 homogenization_RGC_interface4to1 = -1_pInt !-------------------------------------------------------------------------------------------------- ! get the corresponding interface ID in 1D global array if (abs(iFace4D(1)) == 1_pInt) then ! interface with normal //e1 homogenization_RGC_interface4to1 = iFace4D(3) + nGDim(2)*(iFace4D(4)-1_pInt) & + nGDim(2)*nGDim(3)*(iFace4D(2)-1_pInt) if ((iFace4D(2) == 0_pInt) .or. (iFace4D(2) == nGDim(1))) homogenization_RGC_interface4to1 = 0_pInt elseif (abs(iFace4D(1)) == 2_pInt) then ! interface with normal //e2 homogenization_RGC_interface4to1 = iFace4D(4) + nGDim(3)*(iFace4D(2)-1_pInt) & + nGDim(3)*nGDim(1)*(iFace4D(3)-1_pInt) + nIntFace(1) if ((iFace4D(3) == 0_pInt) .or. (iFace4D(3) == nGDim(2))) homogenization_RGC_interface4to1 = 0_pInt elseif (abs(iFace4D(1)) == 3_pInt) then ! interface with normal //e3 homogenization_RGC_interface4to1 = iFace4D(2) + nGDim(1)*(iFace4D(3)-1_pInt) & + nGDim(1)*nGDim(2)*(iFace4D(4)-1_pInt) + nIntFace(1) + nIntFace(2) if ((iFace4D(4) == 0_pInt) .or. (iFace4D(4) == nGDim(3))) homogenization_RGC_interface4to1 = 0_pInt endif end function homogenization_RGC_interface4to1 !-------------------------------------------------------------------------------------------------- !> @brief maps interface ID from 1D (global array) into 4D (normal and local position) !-------------------------------------------------------------------------------------------------- function homogenization_RGC_interface1to4(iFace1D, homID) implicit none integer(pInt), dimension (4) :: homogenization_RGC_interface1to4 integer(pInt), intent(in) :: iFace1D !< interface ID in 1D array integer(pInt), dimension (3) :: nGDim,nIntFace integer(pInt), intent(in) :: homID !< homogenization ID nGDim = homogenization_RGC_Ngrains(:,homID) !-------------------------------------------------------------------------------------------------- ! compute the total number of interfaces, which ... nIntFace(1) = (nGDim(1)-1_pInt)*nGDim(2)*nGDim(3) ! ... normal //e1 nIntFace(2) = nGDim(1)*(nGDim(2)-1_pInt)*nGDim(3) ! ... normal //e2 nIntFace(3) = nGDim(1)*nGDim(2)*(nGDim(3)-1_pInt) ! ... normal //e3 !-------------------------------------------------------------------------------------------------- ! get the corresponding interface ID in 4D (normal and local position) if (iFace1D > 0 .and. iFace1D <= nIntFace(1)) then ! interface with normal //e1 homogenization_RGC_interface1to4(1) = 1_pInt homogenization_RGC_interface1to4(3) = mod((iFace1D-1_pInt),nGDim(2))+1_pInt homogenization_RGC_interface1to4(4) = mod(& int(& real(iFace1D-1_pInt,pReal)/& real(nGDim(2),pReal)& ,pInt)& ,nGDim(3))+1_pInt homogenization_RGC_interface1to4(2) = int(& real(iFace1D-1_pInt,pReal)/& real(nGDim(2),pReal)/& real(nGDim(3),pReal)& ,pInt)+1_pInt elseif (iFace1D > nIntFace(1) .and. iFace1D <= (nIntFace(2) + nIntFace(1))) then ! interface with normal //e2 homogenization_RGC_interface1to4(1) = 2_pInt homogenization_RGC_interface1to4(4) = mod((iFace1D-nIntFace(1)-1_pInt),nGDim(3))+1_pInt homogenization_RGC_interface1to4(2) = mod(& int(& real(iFace1D-nIntFace(1)-1_pInt,pReal)/& real(nGDim(3),pReal)& ,pInt)& ,nGDim(1))+1_pInt homogenization_RGC_interface1to4(3) = int(& real(iFace1D-nIntFace(1)-1_pInt,pReal)/& real(nGDim(3),pReal)/& real(nGDim(1),pReal)& ,pInt)+1_pInt elseif (iFace1D > nIntFace(2) + nIntFace(1) .and. iFace1D <= (nIntFace(3) + nIntFace(2) + nIntFace(1))) then ! interface with normal //e3 homogenization_RGC_interface1to4(1) = 3_pInt homogenization_RGC_interface1to4(2) = mod((iFace1D-nIntFace(2)-nIntFace(1)-1_pInt),nGDim(1))+1_pInt homogenization_RGC_interface1to4(3) = mod(& int(& real(iFace1D-nIntFace(2)-nIntFace(1)-1_pInt,pReal)/& real(nGDim(1),pReal)& ,pInt)& ,nGDim(2))+1_pInt homogenization_RGC_interface1to4(4) = int(& real(iFace1D-nIntFace(2)-nIntFace(1)-1_pInt,pReal)/& real(nGDim(1),pReal)/& real(nGDim(2),pReal)& ,pInt)+1_pInt endif end function homogenization_RGC_interface1to4 !-------------------------------------------------------------------------------------------------- !> @brief calculating the grain deformation gradient (the same with ! homogenization_RGC_partionDeformation, but used only for perturbation scheme) !-------------------------------------------------------------------------------------------------- subroutine homogenization_RGC_grainDeformation(F, avgF, ip, el) use mesh, only: & mesh_element use material, only: & homogenization_maxNgrains,& homogenization_Ngrains, & homogenization_typeInstance implicit none real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F !< partioned F per grain real(pReal), dimension (3,3), intent(in) :: avgF !< integer(pInt), intent(in) :: & el, & !< element number ip !< integration point number real(pReal), dimension (3) :: aVect,nVect integer(pInt), dimension (4) :: intFace integer(pInt), dimension (3) :: iGrain3 integer(pInt) :: homID, iGrain,iFace,i,j integer(pInt), parameter :: nFace = 6_pInt !-------------------------------------------------------------------------------------------------- ! compute the deformation gradient of individual grains due to relaxations homID = homogenization_typeInstance(mesh_element(3,el)) F = 0.0_pReal do iGrain = 1_pInt,homogenization_Ngrains(mesh_element(3,el)) iGrain3 = homogenization_RGC_grain1to3(iGrain,homID) do iFace = 1_pInt,nFace intFace = homogenization_RGC_getInterface(iFace,iGrain3) aVect = homogenization_RGC_relaxationVector(intFace,homID, ip, el) nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) & F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! effective relaxations enddo F(1:3,1:3,iGrain) = F(1:3,1:3,iGrain) + avgF ! relaxed deformation gradient enddo end subroutine homogenization_RGC_grainDeformation end module homogenization_RGC