!-------------------------------------------------------------------------------------------------- !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @author Christoph Kords, Max-Planck-Institut für Eisenforschung GmbH !> @author Chen Zhang, Michigan State University !> @brief crystallite state integration functions and reporting of results !-------------------------------------------------------------------------------------------------- module crystallite use prec, only: & pReal, & pInt use rotations, only: & rotation use FEsolving, only: & FEsolving_execElem, & FEsolving_execIP use material, only: & homogenization_Ngrains implicit none private character(len=64), dimension(:,:), allocatable, private :: & crystallite_output !< name of each post result output integer(pInt), public, protected :: & crystallite_maxSizePostResults !< description not available integer(pInt), dimension(:), allocatable, public, protected :: & crystallite_sizePostResults !< description not available integer(pInt), dimension(:,:), allocatable, private :: & crystallite_sizePostResult !< description not available real(pReal), dimension(:,:,:), allocatable, public :: & crystallite_dt !< requested time increment of each grain real(pReal), dimension(:,:,:), allocatable, private :: & crystallite_subdt, & !< substepped time increment of each grain crystallite_subFrac, & !< already calculated fraction of increment crystallite_subStep !< size of next integration step type(rotation), dimension(:,:,:), allocatable, private :: & crystallite_orientation, & !< orientation crystallite_orientation0 !< initial orientation real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: & crystallite_Fe, & !< current "elastic" def grad (end of converged time step) crystallite_P !< 1st Piola-Kirchhoff stress per grain real(pReal), dimension(:,:,:,:,:), allocatable, public :: & crystallite_S, & !< current 2nd Piola-Kirchhoff stress vector (end of converged time step) crystallite_S0, & !< 2nd Piola-Kirchhoff stress vector at start of FE inc crystallite_partionedS0, & !< 2nd Piola-Kirchhoff stress vector at start of homog inc crystallite_Fp, & !< current plastic def grad (end of converged time step) crystallite_Fp0, & !< plastic def grad at start of FE inc crystallite_partionedFp0,& !< plastic def grad at start of homog inc crystallite_Fi, & !< current intermediate def grad (end of converged time step) crystallite_Fi0, & !< intermediate def grad at start of FE inc crystallite_partionedFi0,& !< intermediate def grad at start of homog inc crystallite_F0, & !< def grad at start of FE inc crystallite_partionedF, & !< def grad to be reached at end of homog inc crystallite_partionedF0, & !< def grad at start of homog inc crystallite_Lp, & !< current plastic velocitiy grad (end of converged time step) crystallite_Lp0, & !< plastic velocitiy grad at start of FE inc crystallite_partionedLp0, & !< plastic velocity grad at start of homog inc crystallite_Li, & !< current intermediate velocitiy grad (end of converged time step) crystallite_Li0, & !< intermediate velocitiy grad at start of FE inc crystallite_partionedLi0 !< intermediate velocity grad at start of homog inc real(pReal), dimension(:,:,:,:,:), allocatable, private :: & crystallite_subS0, & !< 2nd Piola-Kirchhoff stress vector at start of crystallite inc crystallite_invFp, & !< inverse of current plastic def grad (end of converged time step) crystallite_subFp0,& !< plastic def grad at start of crystallite inc crystallite_invFi, & !< inverse of current intermediate def grad (end of converged time step) crystallite_subFi0,& !< intermediate def grad at start of crystallite inc crystallite_subF, & !< def grad to be reached at end of crystallite inc crystallite_subF0, & !< def grad at start of crystallite inc crystallite_subLp0,& !< plastic velocity grad at start of crystallite inc crystallite_subLi0 !< intermediate velocity grad at start of crystallite inc real(pReal), dimension(:,:,:,:,:,:,:), allocatable, public :: & crystallite_dPdF !< current individual dPdF per grain (end of converged time step) logical, dimension(:,:,:), allocatable, public :: & crystallite_requested !< used by upper level (homogenization) to request crystallite calculation logical, dimension(:,:,:), allocatable, private :: & crystallite_converged, & !< convergence flag crystallite_todo, & !< flag to indicate need for further computation crystallite_localPlasticity !< indicates this grain to have purely local constitutive law enum, bind(c) enumerator :: undefined_ID, & phase_ID, & texture_ID, & volume_ID, & orientation_ID, & grainrotation_ID, & defgrad_ID, & fe_ID, & fp_ID, & fi_ID, & lp_ID, & li_ID, & p_ID, & s_ID, & elasmatrix_ID, & neighboringip_ID, & neighboringelement_ID end enum integer(kind(undefined_ID)),dimension(:,:), allocatable, private :: & crystallite_outputID !< ID of each post result output procedure(), pointer :: integrateState public :: & crystallite_init, & crystallite_stress, & crystallite_stressTangent, & crystallite_orientations, & crystallite_push33ToRef, & crystallite_postResults private :: & integrateStress, & integrateState, & integrateStateFPI, & integrateStateEuler, & integrateStateAdaptiveEuler, & integrateStateRK4, & integrateStateRKCK45, & stateJump contains !-------------------------------------------------------------------------------------------------- !> @brief allocates and initialize per grain variables !-------------------------------------------------------------------------------------------------- subroutine crystallite_init #ifdef DEBUG use debug, only: & debug_info, & debug_reset, & debug_level, & debug_crystallite, & debug_levelBasic #endif use numerics, only: & numerics_integrator, & worldrank, & usePingPong use math, only: & math_I3, & math_EulerToR, & math_inv33, & math_mul33x33 use mesh, only: & theMesh, & mesh_element use IO, only: & IO_stringValue, & IO_write_jobFile, & IO_error use material use config, only: & config_deallocate, & config_crystallite, & crystallite_name use constitutive, only: & constitutive_initialFi, & constitutive_microstructure ! derived (shortcut) quantities of given state implicit none integer(pInt), parameter :: FILEUNIT=434_pInt logical, dimension(:,:), allocatable :: devNull integer(pInt) :: & c, & !< counter in integration point component loop i, & !< counter in integration point loop e, & !< counter in element loop o = 0_pInt, & !< counter in output loop r, & cMax, & !< maximum number of integration point components iMax, & !< maximum number of integration points eMax, & !< maximum number of elements myNcomponents, & !< number of components at current IP mySize character(len=65536), dimension(:), allocatable :: str write(6,'(/,a)') ' <<<+- crystallite init -+>>>' cMax = homogenization_maxNgrains iMax = theMesh%elem%nIPs eMax = theMesh%nElems allocate(crystallite_S0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedS0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_S(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subS0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_P(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_F0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedF0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedF(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subF0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subF(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Fp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedFp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subFp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Fp(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_invFp(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Fi0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedFi0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subFi0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Fi(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_invFi(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Fe(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Lp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedLp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subLp0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Lp(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Li0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_partionedLi0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subLi0(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_Li(3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_dPdF(3,3,3,3,cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_dt(cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subdt(cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subFrac(cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_subStep(cMax,iMax,eMax), source=0.0_pReal) allocate(crystallite_orientation(cMax,iMax,eMax)) allocate(crystallite_orientation0(cMax,iMax,eMax)) allocate(crystallite_localPlasticity(cMax,iMax,eMax), source=.true.) allocate(crystallite_requested(cMax,iMax,eMax), source=.false.) allocate(crystallite_todo(cMax,iMax,eMax), source=.false.) allocate(crystallite_converged(cMax,iMax,eMax), source=.true.) allocate(crystallite_output(maxval(crystallite_Noutput), & size(config_crystallite))) ; crystallite_output = '' allocate(crystallite_outputID(maxval(crystallite_Noutput), & size(config_crystallite)), source=undefined_ID) allocate(crystallite_sizePostResults(size(config_crystallite)),source=0_pInt) allocate(crystallite_sizePostResult(maxval(crystallite_Noutput), & size(config_crystallite)), source=0_pInt) select case(numerics_integrator) case(1_pInt) integrateState => integrateStateFPI case(2_pInt) integrateState => integrateStateEuler case(3_pInt) integrateState => integrateStateAdaptiveEuler case(4_pInt) integrateState => integrateStateRK4 case(5_pInt) integrateState => integrateStateRKCK45 end select do c = 1_pInt, size(config_crystallite) #if defined(__GFORTRAN__) str = ['GfortranBug86277'] str = config_crystallite(c)%getStrings('(output)',defaultVal=str) if (str(1) == 'GfortranBug86277') str = [character(len=65536)::] #else str = config_crystallite(c)%getStrings('(output)',defaultVal=[character(len=65536)::]) #endif do o = 1_pInt, size(str) crystallite_output(o,c) = str(o) outputName: select case(str(o)) case ('phase') outputName crystallite_outputID(o,c) = phase_ID case ('texture') outputName crystallite_outputID(o,c) = texture_ID case ('volume') outputName crystallite_outputID(o,c) = volume_ID case ('orientation') outputName crystallite_outputID(o,c) = orientation_ID case ('grainrotation') outputName crystallite_outputID(o,c) = grainrotation_ID case ('defgrad','f') outputName ! ToDo: no alias (f only) crystallite_outputID(o,c) = defgrad_ID case ('fe') outputName crystallite_outputID(o,c) = fe_ID case ('fp') outputName crystallite_outputID(o,c) = fp_ID case ('fi') outputName crystallite_outputID(o,c) = fi_ID case ('lp') outputName crystallite_outputID(o,c) = lp_ID case ('li') outputName crystallite_outputID(o,c) = li_ID case ('p','firstpiola','1stpiola') outputName ! ToDo: no alias (p only) crystallite_outputID(o,c) = p_ID case ('s','tstar','secondpiola','2ndpiola') outputName ! ToDo: no alias (s only) crystallite_outputID(o,c) = s_ID case ('elasmatrix') outputName crystallite_outputID(o,c) = elasmatrix_ID case ('neighboringip') outputName ! ToDo: this is not a result, it is static. Should be written out by mesh crystallite_outputID(o,c) = neighboringip_ID case ('neighboringelement') outputName ! ToDo: this is not a result, it is static. Should be written out by mesh crystallite_outputID(o,c) = neighboringelement_ID case default outputName call IO_error(105_pInt,ext_msg=trim(str(o))//' (Crystallite)') end select outputName enddo enddo do r = 1_pInt,size(config_crystallite) do o = 1_pInt,crystallite_Noutput(r) select case(crystallite_outputID(o,r)) case(phase_ID,texture_ID,volume_ID) mySize = 1_pInt case(orientation_ID,grainrotation_ID) mySize = 4_pInt case(defgrad_ID,fe_ID,fp_ID,fi_ID,lp_ID,li_ID,p_ID,s_ID) mySize = 9_pInt case(elasmatrix_ID) mySize = 36_pInt case(neighboringip_ID,neighboringelement_ID) mySize = theMesh%elem%nIPneighbors case default mySize = 0_pInt end select crystallite_sizePostResult(o,r) = mySize crystallite_sizePostResults(r) = crystallite_sizePostResults(r) + mySize enddo enddo crystallite_maxSizePostResults = & maxval(crystallite_sizePostResults(microstructure_crystallite),microstructure_active) !-------------------------------------------------------------------------------------------------- ! write description file for crystallite output if (worldrank == 0_pInt) then call IO_write_jobFile(FILEUNIT,'outputCrystallite') do r = 1_pInt,size(config_crystallite) if (any(microstructure_crystallite(mesh_element(4,:)) == r)) then write(FILEUNIT,'(/,a,/)') '['//trim(crystallite_name(r))//']' do o = 1_pInt,crystallite_Noutput(r) write(FILEUNIT,'(a,i4)') trim(crystallite_output(o,r))//char(9),crystallite_sizePostResult(o,r) enddo endif enddo close(FILEUNIT) endif call config_deallocate('material.config/crystallite') !-------------------------------------------------------------------------------------------------- ! initialize !$OMP PARALLEL DO PRIVATE(myNcomponents,i,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) myNcomponents = homogenization_Ngrains(mesh_element(3,e)) forall (i = FEsolving_execIP(1,e):FEsolving_execIP(2,e), c = 1_pInt:myNcomponents) crystallite_Fp0(1:3,1:3,c,i,e) = math_EulerToR(material_EulerAngles(1:3,c,i,e)) ! plastic def gradient reflects init orientation crystallite_Fi0(1:3,1:3,c,i,e) = constitutive_initialFi(c,i,e) crystallite_F0(1:3,1:3,c,i,e) = math_I3 crystallite_localPlasticity(c,i,e) = phase_localPlasticity(material_phase(c,i,e)) crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(math_mul33x33(crystallite_Fi0(1:3,1:3,c,i,e), & crystallite_Fp0(1:3,1:3,c,i,e))) ! assuming that euler angles are given in internal strain free configuration crystallite_Fp(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) crystallite_Fi(1:3,1:3,c,i,e) = crystallite_Fi0(1:3,1:3,c,i,e) crystallite_requested(c,i,e) = .true. endforall enddo !$OMP END PARALLEL DO if(any(.not. crystallite_localPlasticity) .and. .not. usePingPong) call IO_error(601_pInt) ! exit if nonlocal but no ping-pong ToDo: Why not check earlier? or in nonlocal? crystallite_partionedFp0 = crystallite_Fp0 crystallite_partionedFi0 = crystallite_Fi0 crystallite_partionedF0 = crystallite_F0 crystallite_partionedF = crystallite_F0 call crystallite_orientations() crystallite_orientation0 = crystallite_orientation ! store initial orientations for calculation of grain rotations !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do c = 1_pInt,homogenization_Ngrains(mesh_element(3,e)) call constitutive_microstructure(crystallite_Fe(1:3,1:3,c,i,e), & crystallite_Fp(1:3,1:3,c,i,e), & c,i,e) ! update dependent state variables to be consistent with basic states enddo enddo enddo !$OMP END PARALLEL DO devNull = crystallite_stress() call crystallite_stressTangent #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) then write(6,'(a42,1x,i10)') ' # of elements: ', eMax write(6,'(a42,1x,i10)') 'max # of integration points/element: ', iMax write(6,'(a42,1x,i10)') 'max # of constituents/integration point: ', cMax write(6,'(a42,1x,i10)') 'max # of neigbours/integration point: ', theMesh%elem%nIPneighbors write(6,'(a42,1x,i10)') ' # of nonlocal constituents: ',count(.not. crystallite_localPlasticity) flush(6) endif call debug_info call debug_reset #endif end subroutine crystallite_init !-------------------------------------------------------------------------------------------------- !> @brief calculate stress (P) !-------------------------------------------------------------------------------------------------- function crystallite_stress(dummyArgumentToPreventInternalCompilerErrorWithGCC) use prec, only: & tol_math_check, & dNeq0 use numerics, only: & subStepMinCryst, & subStepSizeCryst, & stepIncreaseCryst #ifdef DEBUG use debug, only: & debug_level, & debug_crystallite, & debug_levelBasic, & debug_levelExtensive, & debug_levelSelective, & debug_e, & debug_i, & debug_g #endif use IO, only: & IO_warning, & IO_error use math, only: & math_inv33, & math_mul33x33 use mesh, only: & theMesh, & mesh_element use material, only: & homogenization_Ngrains, & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt implicit none logical, dimension(theMesh%elem%nIPs,theMesh%Nelems) :: crystallite_stress real(pReal), intent(in), optional :: & dummyArgumentToPreventInternalCompilerErrorWithGCC real(pReal) :: & formerSubStep integer(pInt) :: & NiterationCrystallite, & ! number of iterations in crystallite loop c, & !< counter in integration point component loop i, & !< counter in integration point loop e, & !< counter in element loop startIP, endIP, & s #ifdef DEBUG if (iand(debug_level(debug_crystallite),debug_levelSelective) /= 0_pInt & .and. FEsolving_execElem(1) <= debug_e & .and. debug_e <= FEsolving_execElem(2)) then write(6,'(/,a,i8,1x,i2,1x,i3)') '<< CRYST stress >> boundary and initial values at el ip ipc ', & debug_e,debug_i, debug_g write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> F ', & transpose(crystallite_partionedF(1:3,1:3,debug_g,debug_i,debug_e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> F0 ', & transpose(crystallite_partionedF0(1:3,1:3,debug_g,debug_i,debug_e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Fp0', & transpose(crystallite_partionedFp0(1:3,1:3,debug_g,debug_i,debug_e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Fi0', & transpose(crystallite_partionedFi0(1:3,1:3,debug_g,debug_i,debug_e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Lp0', & transpose(crystallite_partionedLp0(1:3,1:3,debug_g,debug_i,debug_e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Li0', & transpose(crystallite_partionedLi0(1:3,1:3,debug_g,debug_i,debug_e)) endif #endif !-------------------------------------------------------------------------------------------------- ! initialize to starting condition crystallite_subStep = 0.0_pReal !$OMP PARALLEL DO elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e); do c = 1_pInt,homogenization_Ngrains(mesh_element(3,e)) homogenizationRequestsCalculation: if (crystallite_requested(c,i,e)) then plasticState (phaseAt(c,i,e))%subState0( :,phasememberAt(c,i,e)) = & plasticState (phaseAt(c,i,e))%partionedState0(:,phasememberAt(c,i,e)) do s = 1_pInt, phase_Nsources(phaseAt(c,i,e)) sourceState(phaseAt(c,i,e))%p(s)%subState0( :,phasememberAt(c,i,e)) = & sourceState(phaseAt(c,i,e))%p(s)%partionedState0(:,phasememberAt(c,i,e)) enddo crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_partionedFp0(1:3,1:3,c,i,e) crystallite_subLp0(1:3,1:3,c,i,e) = crystallite_partionedLp0(1:3,1:3,c,i,e) crystallite_subFi0(1:3,1:3,c,i,e) = crystallite_partionedFi0(1:3,1:3,c,i,e) crystallite_subLi0(1:3,1:3,c,i,e) = crystallite_partionedLi0(1:3,1:3,c,i,e) crystallite_subF0(1:3,1:3,c,i,e) = crystallite_partionedF0(1:3,1:3,c,i,e) crystallite_subS0(1:3,1:3,c,i,e) = crystallite_partionedS0(1:3,1:3,c,i,e) crystallite_subFrac(c,i,e) = 0.0_pReal crystallite_subStep(c,i,e) = 1.0_pReal/subStepSizeCryst crystallite_todo(c,i,e) = .true. crystallite_converged(c,i,e) = .false. ! pretend failed step of 1/subStepSizeCryst endif homogenizationRequestsCalculation enddo; enddo enddo elementLooping1 !$OMP END PARALLEL DO singleRun: if (FEsolving_execELem(1) == FEsolving_execElem(2) .and. & FEsolving_execIP(1,FEsolving_execELem(1))==FEsolving_execIP(2,FEsolving_execELem(1))) then startIP = FEsolving_execIP(1,FEsolving_execELem(1)) endIP = startIP else singleRun startIP = 1_pInt endIP = theMesh%elem%nIPs endif singleRun NiterationCrystallite = 0_pInt cutbackLooping: do while (any(crystallite_todo(:,startIP:endIP,FEsolving_execELem(1):FEsolving_execElem(2)))) NiterationCrystallite = NiterationCrystallite + 1_pInt #ifdef DEBUG if (iand(debug_level(debug_crystallite),debug_levelExtensive) /= 0_pInt) & write(6,'(a,i6)') '<< CRYST stress >> crystallite iteration ',NiterationCrystallite #endif !$OMP PARALLEL DO PRIVATE(formerSubStep) elementLooping3: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do c = 1,homogenization_Ngrains(mesh_element(3,e)) !-------------------------------------------------------------------------------------------------- ! wind forward if (crystallite_converged(c,i,e)) then formerSubStep = crystallite_subStep(c,i,e) crystallite_subFrac(c,i,e) = crystallite_subFrac(c,i,e) + crystallite_subStep(c,i,e) crystallite_subStep(c,i,e) = min(1.0_pReal - crystallite_subFrac(c,i,e), & stepIncreaseCryst * crystallite_subStep(c,i,e)) crystallite_todo(c,i,e) = crystallite_subStep(c,i,e) > 0.0_pReal ! still time left to integrate on? if (crystallite_todo(c,i,e)) then crystallite_subF0 (1:3,1:3,c,i,e) = crystallite_subF(1:3,1:3,c,i,e) crystallite_subLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e) crystallite_subLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e) crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e) crystallite_subFi0(1:3,1:3,c,i,e) = crystallite_Fi (1:3,1:3,c,i,e) crystallite_subS0 (1:3,1:3,c,i,e) = crystallite_S (1:3,1:3,c,i,e) !if abbrevation, make c and p private in omp plasticState( phaseAt(c,i,e))%subState0(:,phasememberAt(c,i,e)) & = plasticState(phaseAt(c,i,e))%state( :,phasememberAt(c,i,e)) do s = 1_pInt, phase_Nsources(phaseAt(c,i,e)) sourceState( phaseAt(c,i,e))%p(s)%subState0(:,phasememberAt(c,i,e)) & = sourceState(phaseAt(c,i,e))%p(s)%state( :,phasememberAt(c,i,e)) enddo #ifdef DEBUG if (iand(debug_level(debug_crystallite),debug_levelBasic) /= 0_pInt & .and. ((e == debug_e .and. i == debug_i .and. c == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) & write(6,'(a,f12.8,a,f12.8,a,i8,1x,i2,1x,i3,/)') '<< CRYST stress >> winding forward from ', & crystallite_subFrac(c,i,e)-formerSubStep,' to current crystallite_subfrac ', & crystallite_subFrac(c,i,e),' in crystallite_stress at el ip ipc ',e,i,c #endif endif !-------------------------------------------------------------------------------------------------- ! cut back (reduced time and restore) else crystallite_subStep(c,i,e) = subStepSizeCryst * crystallite_subStep(c,i,e) crystallite_Fp (1:3,1:3,c,i,e) = crystallite_subFp0(1:3,1:3,c,i,e) crystallite_invFp(1:3,1:3,c,i,e) = math_inv33(crystallite_Fp (1:3,1:3,c,i,e)) crystallite_Fi (1:3,1:3,c,i,e) = crystallite_subFi0(1:3,1:3,c,i,e) crystallite_invFi(1:3,1:3,c,i,e) = math_inv33(crystallite_Fi (1:3,1:3,c,i,e)) crystallite_S (1:3,1:3,c,i,e) = crystallite_S0 (1:3,1:3,c,i,e) if (crystallite_subStep(c,i,e) < 1.0_pReal) then ! actual (not initial) cutback crystallite_Lp (1:3,1:3,c,i,e) = crystallite_subLp0(1:3,1:3,c,i,e) crystallite_Li (1:3,1:3,c,i,e) = crystallite_subLi0(1:3,1:3,c,i,e) endif plasticState (phaseAt(c,i,e))%state( :,phasememberAt(c,i,e)) & = plasticState(phaseAt(c,i,e))%subState0(:,phasememberAt(c,i,e)) do s = 1_pInt, phase_Nsources(phaseAt(c,i,e)) sourceState( phaseAt(c,i,e))%p(s)%state( :,phasememberAt(c,i,e)) & = sourceState(phaseAt(c,i,e))%p(s)%subState0(:,phasememberAt(c,i,e)) enddo ! cant restore dotState here, since not yet calculated in first cutback after initialization crystallite_todo(c,i,e) = crystallite_subStep(c,i,e) > subStepMinCryst ! still on track or already done (beyond repair) #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((e == debug_e .and. i == debug_i .and. c == debug_g) & .or. .not. iand(debug_level(debug_crystallite),debug_levelSelective) /= 0_pInt)) then if (crystallite_todo(c,i,e)) then write(6,'(a,f12.8,a,i8,1x,i2,1x,i3,/)') '<< CRYST stress >> cutback with new crystallite_subStep: ', & crystallite_subStep(c,i,e),' at el ip ipc ',e,i,c else write(6,'(a,i8,1x,i2,1x,i3,/)') '<< CRYST stress >> reached minimum step size at el ip ipc ',e,i,c endif endif #endif endif !-------------------------------------------------------------------------------------------------- ! prepare for integration if (crystallite_todo(c,i,e)) then crystallite_subF(1:3,1:3,c,i,e) = crystallite_subF0(1:3,1:3,c,i,e) & + crystallite_subStep(c,i,e) * (crystallite_partionedF (1:3,1:3,c,i,e) & - crystallite_partionedF0(1:3,1:3,c,i,e)) crystallite_Fe(1:3,1:3,c,i,e) = math_mul33x33(math_mul33x33(crystallite_subF (1:3,1:3,c,i,e), & crystallite_invFp(1:3,1:3,c,i,e)), & crystallite_invFi(1:3,1:3,c,i,e)) crystallite_subdt(c,i,e) = crystallite_subStep(c,i,e) * crystallite_dt(c,i,e) crystallite_converged(c,i,e) = .false. endif enddo enddo enddo elementLooping3 !$OMP END PARALLEL DO #ifdef DEBUG if (iand(debug_level(debug_crystallite),debug_levelExtensive) /= 0_pInt) then write(6,'(/,a,f8.5,a,f8.5,/)') '<< CRYST stress >> ',minval(crystallite_subStep), & ' ≤ subStep ≤ ',maxval(crystallite_subStep) write(6,'(/,a,f8.5,a,f8.5,/)') '<< CRYST stress >> ',minval(crystallite_subFrac), & ' ≤ subFrac ≤ ',maxval(crystallite_subFrac) flush(6) if (iand(debug_level(debug_crystallite),debug_levelSelective) /= 0_pInt) then write(6,'(/,a,f8.5,1x,a,1x,f8.5,1x,a)') '<< CRYST stress >> subFrac + subStep = ',& crystallite_subFrac(debug_g,debug_i,debug_e),'+',crystallite_subStep(debug_g,debug_i,debug_e),'@selective' flush(6) endif endif #endif !-------------------------------------------------------------------------------------------------- ! integrate --- requires fully defined state array (basic + dependent state) if (any(crystallite_todo)) call integrateState() ! TODO: unroll into proper elementloop to avoid N^2 for single point evaluation where(.not. crystallite_converged .and. crystallite_subStep > subStepMinCryst) & ! do not try non-converged but fully cutbacked any further crystallite_todo = .true. ! TODO: again unroll this into proper elementloop to avoid N^2 for single point evaluation enddo cutbackLooping ! return whether converged or not crystallite_stress = .false. elementLooping5: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) crystallite_stress(i,e) = all(crystallite_converged(:,i,e)) enddo enddo elementLooping5 #ifdef DEBUG elementLooping6: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do c = 1,homogenization_Ngrains(mesh_element(3,e)) if (.not. crystallite_converged(c,i,e)) then if(iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i8,1x,i2,1x,i3,/)') '<< CRYST stress >> no convergence at el ip ipc ', & e,i,c endif if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((e == debug_e .and. i == debug_i .and. c == debug_g) & .or. .not. iand(debug_level(debug_crystallite),debug_levelSelective) /= 0_pInt)) then write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST stress >> solution at el ip ipc ',e,i,c write(6,'(/,a,/,3(12x,3(f12.4,1x)/))') '<< CRYST stress >> P / MPa', & transpose(crystallite_P(1:3,1:3,c,i,e))*1.0e-6_pReal write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Fp', & transpose(crystallite_Fp(1:3,1:3,c,i,e)) write(6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST stress >> Fi', & transpose(crystallite_Fi(1:3,1:3,c,i,e)) write(6,'(a,/,3(12x,3(f14.9,1x)/),/)') '<< CRYST stress >> Lp', & transpose(crystallite_Lp(1:3,1:3,c,i,e)) write(6,'(a,/,3(12x,3(f14.9,1x)/),/)') '<< CRYST stress >> Li', & transpose(crystallite_Li(1:3,1:3,c,i,e)) flush(6) endif enddo enddo enddo elementLooping6 #endif end function crystallite_stress !-------------------------------------------------------------------------------------------------- !> @brief calculate tangent (dPdF) !-------------------------------------------------------------------------------------------------- subroutine crystallite_stressTangent() use prec, only: & tol_math_check, & dNeq0 use IO, only: & IO_warning, & IO_error use math, only: & math_inv33, & math_identity2nd, & math_mul33x33, & math_3333to99, & math_99to3333, & math_I3, & math_mul3333xx3333, & math_mul33xx33, & math_invert2, & math_det33 use mesh, only: & mesh_element use material, only: & homogenization_Ngrains use constitutive, only: & constitutive_SandItsTangents, & constitutive_LpAndItsTangents, & constitutive_LiAndItsTangents implicit none integer(pInt) :: & c, & !< counter in integration point component loop i, & !< counter in integration point loop e, & !< counter in element loop o, & p real(pReal), dimension(3,3) :: temp_33_1, devNull,invSubFi0, temp_33_2, temp_33_3, temp_33_4 real(pReal), dimension(3,3,3,3) :: dSdFe, & dSdF, & dSdFi, & dLidS, & dLidFi, & dLpdS, & dLpdFi, & dFidS, & dFpinvdF, & rhs_3333, & lhs_3333, & temp_3333 real(pReal), dimension(9,9):: temp_99 logical :: error !$OMP PARALLEL DO PRIVATE(dSdF,dSdFe,dSdFi,dLpdS,dLpdFi,dFpinvdF,dLidS,dLidFi,dFidS,invSubFi0,o,p, & !$OMP rhs_3333,lhs_3333,temp_99,temp_33_1,temp_33_2,temp_33_3,temp_33_4,temp_3333,error) elementLooping: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do c = 1_pInt,homogenization_Ngrains(mesh_element(3,e)) call constitutive_SandItsTangents(devNull,dSdFe,dSdFi, & crystallite_Fe(1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e),c,i,e) ! call constitutive law to calculate elastic stress tangent call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, & crystallite_S (1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e), & c,i,e) ! call constitutive law to calculate Li tangent in lattice configuration if (sum(abs(dLidS)) < tol_math_check) then dFidS = 0.0_pReal else invSubFi0 = math_inv33(crystallite_subFi0(1:3,1:3,c,i,e)) lhs_3333 = 0.0_pReal; rhs_3333 = 0.0_pReal do o=1_pInt,3_pInt; do p=1_pInt,3_pInt lhs_3333(1:3,1:3,o,p) = lhs_3333(1:3,1:3,o,p) & + crystallite_subdt(c,i,e)*math_mul33x33(invSubFi0,dLidFi(1:3,1:3,o,p)) lhs_3333(1:3,o,1:3,p) = lhs_3333(1:3,o,1:3,p) & + crystallite_invFi(1:3,1:3,c,i,e)*crystallite_invFi(p,o,c,i,e) rhs_3333(1:3,1:3,o,p) = rhs_3333(1:3,1:3,o,p) & - crystallite_subdt(c,i,e)*math_mul33x33(invSubFi0,dLidS(1:3,1:3,o,p)) enddo;enddo call math_invert2(temp_99,error,math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600_pInt,el=e,ip=i,g=c, & ext_msg='inversion error in analytic tangent calculation') dFidS = 0.0_pReal else dFidS = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif dLidS = math_mul3333xx3333(dLidFi,dFidS) + dLidS endif call constitutive_LpAndItsTangents(devNull,dLpdS,dLpdFi, & crystallite_S (1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e),c,i,e) ! call constitutive law to calculate Lp tangent in lattice configuration dLpdS = math_mul3333xx3333(dLpdFi,dFidS) + dLpdS !-------------------------------------------------------------------------------------------------- ! calculate dSdF temp_33_1 = transpose(math_mul33x33(crystallite_invFp(1:3,1:3,c,i,e), & crystallite_invFi(1:3,1:3,c,i,e))) temp_33_2 = math_mul33x33( crystallite_subF (1:3,1:3,c,i,e), & math_inv33(crystallite_subFp0(1:3,1:3,c,i,e))) temp_33_3 = math_mul33x33(math_mul33x33(crystallite_subF (1:3,1:3,c,i,e), & crystallite_invFp (1:3,1:3,c,i,e)), & math_inv33(crystallite_subFi0(1:3,1:3,c,i,e))) forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) rhs_3333(p,o,1:3,1:3) = math_mul33x33(dSdFe(p,o,1:3,1:3),temp_33_1) temp_3333(1:3,1:3,p,o) = math_mul33x33(math_mul33x33(temp_33_2,dLpdS(1:3,1:3,p,o)), & crystallite_invFi(1:3,1:3,c,i,e)) & + math_mul33x33(temp_33_3,dLidS(1:3,1:3,p,o)) end forall lhs_3333 = crystallite_subdt(c,i,e)*math_mul3333xx3333(dSdFe,temp_3333) & + math_mul3333xx3333(dSdFi,dFidS) call math_invert2(temp_99,error,math_identity2nd(9_pInt)+math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600_pInt,el=e,ip=i,g=c, & ext_msg='inversion error in analytic tangent calculation') dSdF = rhs_3333 else dSdF = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif !-------------------------------------------------------------------------------------------------- ! calculate dFpinvdF temp_3333 = math_mul3333xx3333(dLpdS,dSdF) forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) dFpinvdF(1:3,1:3,p,o) & = -crystallite_subdt(c,i,e) & * math_mul33x33(math_inv33(crystallite_subFp0(1:3,1:3,c,i,e)), & math_mul33x33(temp_3333(1:3,1:3,p,o),crystallite_invFi(1:3,1:3,c,i,e))) end forall !-------------------------------------------------------------------------------------------------- ! assemble dPdF temp_33_1 = math_mul33x33(crystallite_invFp(1:3,1:3,c,i,e), & math_mul33x33(crystallite_S(1:3,1:3,c,i,e), & transpose(crystallite_invFp(1:3,1:3,c,i,e)))) temp_33_2 = math_mul33x33(crystallite_S(1:3,1:3,c,i,e), & transpose(crystallite_invFp(1:3,1:3,c,i,e))) temp_33_3 = math_mul33x33(crystallite_subF(1:3,1:3,c,i,e), & crystallite_invFp(1:3,1:3,c,i,e)) temp_33_4 = math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,c,i,e), & crystallite_invFp(1:3,1:3,c,i,e)), & crystallite_S(1:3,1:3,c,i,e)) crystallite_dPdF(1:3,1:3,1:3,1:3,c,i,e) = 0.0_pReal do p=1_pInt, 3_pInt crystallite_dPdF(p,1:3,p,1:3,c,i,e) = transpose(temp_33_1) enddo forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) crystallite_dPdF(1:3,1:3,p,o,c,i,e) = crystallite_dPdF(1:3,1:3,p,o,c,i,e) + & math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,c,i,e),dFpinvdF(1:3,1:3,p,o)),temp_33_2) + & math_mul33x33(math_mul33x33(temp_33_3,dSdF(1:3,1:3,p,o)),transpose(crystallite_invFp(1:3,1:3,c,i,e))) + & math_mul33x33(temp_33_4,transpose(dFpinvdF(1:3,1:3,p,o))) end forall enddo; enddo enddo elementLooping !$OMP END PARALLEL DO end subroutine crystallite_stressTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates orientations !-------------------------------------------------------------------------------------------------- subroutine crystallite_orientations use math, only: & math_rotationalPart33, & math_RtoQ use material, only: & plasticState, & material_phase, & homogenization_Ngrains use mesh, only: & mesh_element use lattice, only: & lattice_qDisorientation use plastic_nonlocal, only: & plastic_nonlocal_updateCompatibility implicit none integer(pInt) & c, & !< counter in integration point component loop i, & !< counter in integration point loop e !< counter in element loop !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do c = 1_pInt,homogenization_Ngrains(mesh_element(3,e)) call crystallite_orientation(c,i,e)%fromRotationMatrix(transpose(math_rotationalPart33(crystallite_Fe(1:3,1:3,c,i,e)))) enddo; enddo; enddo !$OMP END PARALLEL DO ! --- we use crystallite_orientation from above, so need a separate loop nonlocalPresent: if (any(plasticState%nonLocal)) then !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) if (plasticState(material_phase(1,i,e))%nonLocal) & ! if nonlocal model call plastic_nonlocal_updateCompatibility(crystallite_orientation,i,e) enddo; enddo !$OMP END PARALLEL DO endif nonlocalPresent end subroutine crystallite_orientations !-------------------------------------------------------------------------------------------------- !> @brief Map 2nd order tensor to reference config !-------------------------------------------------------------------------------------------------- function crystallite_push33ToRef(ipc,ip,el, tensor33) use math, only: & math_mul33x33, & math_inv33, & math_EulerToR use material, only: & material_EulerAngles ! ToDo: Why stored? We also have crystallite_orientation0 implicit none real(pReal), dimension(3,3) :: crystallite_push33ToRef real(pReal), dimension(3,3), intent(in) :: tensor33 real(pReal), dimension(3,3) :: T integer(pInt), intent(in):: & el, & ! element index ip, & ! integration point index ipc ! grain index T = math_mul33x33(math_EulerToR(material_EulerAngles(1:3,ipc,ip,el)), & transpose(math_inv33(crystallite_subF(1:3,1:3,ipc,ip,el)))) crystallite_push33ToRef = math_mul33x33(transpose(T),math_mul33x33(tensor33,T)) end function crystallite_push33ToRef !-------------------------------------------------------------------------------------------------- !> @brief return results of particular grain !-------------------------------------------------------------------------------------------------- function crystallite_postResults(ipc, ip, el) use math, only: & math_qToEuler, & math_qToEulerAxisAngle, & math_mul33x33, & math_det33, & math_I3, & inDeg use mesh, only: & theMesh, & mesh_element, & mesh_ipVolume, & mesh_ipNeighborhood use material, only: & plasticState, & sourceState, & microstructure_crystallite, & crystallite_Noutput, & material_phase, & material_texture, & homogenization_Ngrains use constitutive, only: & constitutive_homogenizedC, & constitutive_postResults use rotations, only: & rotation implicit none integer(pInt), intent(in):: & el, & !< element index ip, & !< integration point index ipc !< grain index real(pReal), dimension(1+crystallite_sizePostResults(microstructure_crystallite(mesh_element(4,el))) + & 1+plasticState(material_phase(ipc,ip,el))%sizePostResults + & sum(sourceState(material_phase(ipc,ip,el))%p(:)%sizePostResults)) :: & crystallite_postResults real(pReal) :: & detF integer(pInt) :: & o, & c, & crystID, & mySize, & n type(rotation) :: rot crystID = microstructure_crystallite(mesh_element(4,el)) crystallite_postResults = 0.0_pReal crystallite_postResults(1) = real(crystallite_sizePostResults(crystID),pReal) ! header-like information (length) c = 1_pInt do o = 1_pInt,crystallite_Noutput(crystID) mySize = 0_pInt select case(crystallite_outputID(o,crystID)) case (phase_ID) mySize = 1_pInt crystallite_postResults(c+1) = real(material_phase(ipc,ip,el),pReal) ! phaseID of grain case (texture_ID) mySize = 1_pInt crystallite_postResults(c+1) = real(material_texture(ipc,ip,el),pReal) ! textureID of grain case (volume_ID) mySize = 1_pInt detF = math_det33(crystallite_partionedF(1:3,1:3,ipc,ip,el)) ! V_current = det(F) * V_reference crystallite_postResults(c+1) = detF * mesh_ipVolume(ip,el) & / real(homogenization_Ngrains(mesh_element(3,el)),pReal) ! grain volume (not fraction but absolute) case (orientation_ID) mySize = 4_pInt crystallite_postResults(c+1:c+mySize) = crystallite_orientation(ipc,ip,el)%asQuaternion() case (grainrotation_ID) rot = crystallite_orientation0(ipc,ip,el)%misorientation(crystallite_orientation(ipc,ip,el)) mySize = 4_pInt crystallite_postResults(c+1:c+mySize) = rot%asAxisAnglePair() crystallite_postResults(c+4) = inDeg * crystallite_postResults(c+4) ! angle in degree ! remark: tensor output is of the form 11,12,13, 21,22,23, 31,32,33 ! thus row index i is slow, while column index j is fast. reminder: "row is slow" case (defgrad_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_partionedF(1:3,1:3,ipc,ip,el)),[mySize]) case (fe_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_Fe(1:3,1:3,ipc,ip,el)),[mySize]) case (fp_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_Fp(1:3,1:3,ipc,ip,el)),[mySize]) case (fi_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_Fi(1:3,1:3,ipc,ip,el)),[mySize]) case (lp_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_Lp(1:3,1:3,ipc,ip,el)),[mySize]) case (li_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_Li(1:3,1:3,ipc,ip,el)),[mySize]) case (p_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(transpose(crystallite_P(1:3,1:3,ipc,ip,el)),[mySize]) case (s_ID) mySize = 9_pInt crystallite_postResults(c+1:c+mySize) = & reshape(crystallite_S(1:3,1:3,ipc,ip,el),[mySize]) case (elasmatrix_ID) mySize = 36_pInt crystallite_postResults(c+1:c+mySize) = reshape(constitutive_homogenizedC(ipc,ip,el),[mySize]) case(neighboringelement_ID) mySize = theMesh%elem%nIPneighbors crystallite_postResults(c+1:c+mySize) = 0.0_pReal forall (n = 1_pInt:mySize) & crystallite_postResults(c+n) = real(mesh_ipNeighborhood(1,n,ip,el),pReal) case(neighboringip_ID) mySize = theMesh%elem%nIPneighbors crystallite_postResults(c+1:c+mySize) = 0.0_pReal forall (n = 1_pInt:mySize) & crystallite_postResults(c+n) = real(mesh_ipNeighborhood(2,n,ip,el),pReal) end select c = c + mySize enddo crystallite_postResults(c+1) = real(plasticState(material_phase(ipc,ip,el))%sizePostResults,pReal) ! size of constitutive results c = c + 1_pInt if (size(crystallite_postResults)-c > 0_pInt) & crystallite_postResults(c+1:size(crystallite_postResults)) = & constitutive_postResults(crystallite_S(1:3,1:3,ipc,ip,el), crystallite_Fi(1:3,1:3,ipc,ip,el), & ipc, ip, el) end function crystallite_postResults !-------------------------------------------------------------------------------------------------- !> @brief calculation of stress (P) with time integration based on a residuum in Lp and !> intermediate acceleration of the Newton-Raphson correction !-------------------------------------------------------------------------------------------------- logical function integrateStress(& ipc,& ! grain number ip,& ! integration point number el,& ! element number timeFraction & ) use, intrinsic :: & IEEE_arithmetic use prec, only: tol_math_check, & dEq0 use numerics, only: nStress, & aTol_crystalliteStress, & rTol_crystalliteStress, & iJacoLpresiduum, & subStepSizeLp, & subStepSizeLi #ifdef DEBUG use debug, only: debug_level, & debug_e, & debug_i, & debug_g, & debug_crystallite, & debug_levelBasic, & debug_levelExtensive, & debug_levelSelective #endif use constitutive, only: constitutive_LpAndItsTangents, & constitutive_LiAndItsTangents, & constitutive_SandItsTangents use math, only: math_mul33x33, & #ifdef __PGI norm2, & #endif math_mul33xx33, & math_mul3333xx3333, & math_inv33, & math_det33, & math_I3, & math_identity2nd, & math_3333to99, & math_33to9, & math_9to33 implicit none integer(pInt), intent(in):: el, & ! element index ip, & ! integration point index ipc ! grain index real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep real(pReal), dimension(3,3):: Fg_new, & ! deformation gradient at end of timestep Fp_new, & ! plastic deformation gradient at end of timestep Fe_new, & ! elastic deformation gradient at end of timestep invFp_new, & ! inverse of Fp_new Fi_new, & ! gradient of intermediate deformation stages invFi_new, & invFp_current, & ! inverse of Fp_current invFi_current, & ! inverse of Fp_current Lpguess, & ! current guess for plastic velocity gradient Lpguess_old, & ! known last good guess for plastic velocity gradient Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law residuumLp, & ! current residuum of plastic velocity gradient residuumLp_old, & ! last residuum of plastic velocity gradient deltaLp, & ! direction of next guess Liguess, & ! current guess for intermediate velocity gradient Liguess_old, & ! known last good guess for intermediate velocity gradient Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law residuumLi, & ! current residuum of intermediate velocity gradient residuumLi_old, & ! last residuum of intermediate velocity gradient deltaLi, & ! direction of next guess S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration A, & B, & Fe, & ! elastic deformation gradient temp_33 real(pReal), dimension(9):: work ! needed for matrix inversion by LAPACK integer(pInt), dimension(9) :: devNull ! needed for matrix inversion by LAPACK real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme) dRLp_dLp2, & ! working copy of dRdLp dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme) real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress dS_dFi, & dFe_dLp, & ! partial derivative of elastic deformation gradient dFe_dLi, & dFi_dLi, & dLp_dFi, & dLi_dFi, & dLp_dS, & dLi_dS real(pReal) detInvFi, & ! determinant of InvFi steplengthLp, & steplengthLi, & dt, & ! time increment aTolLp, & aTolLi integer(pInt) NiterationStressLp, & ! number of stress integrations NiterationStressLi, & ! number of inner stress integrations ierr, & ! error indicator for LAPACK o, & p, & jacoCounterLp, & jacoCounterLi ! counters to check for Jacobian update external :: & dgesv !* be pessimistic integrateStress = .false. #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) & write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> at el ip ipc ',el,ip,ipc #endif if (present(timeFraction)) then dt = crystallite_subdt(ipc,ip,el) * timeFraction Fg_new = crystallite_subF0(1:3,1:3,ipc,ip,el) & + (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction else dt = crystallite_subdt(ipc,ip,el) Fg_new = crystallite_subF(1:3,1:3,ipc,ip,el) endif !* feed local variables Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! ... and take it as first guess Liguess = crystallite_Li(1:3,1:3,ipc,ip,el) ! ... and take it as first guess Liguess_old = Liguess invFp_current = math_inv33(crystallite_subFp0(1:3,1:3,ipc,ip,el)) failedInversionFp: if (all(dEq0(invFp_current))) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> failed on inversion of current Fp at el ip ipc ',& el,ip,ipc if (iand(debug_level(debug_crystallite), debug_levelExtensive) > 0_pInt) & write(6,'(/,a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> current Fp ',transpose(crystallite_subFp0(1:3,1:3,ipc,ip,el)) #endif return endif failedInversionFp A = math_mul33x33(Fg_new,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp invFi_current = math_inv33(crystallite_subFi0(1:3,1:3,ipc,ip,el)) failedInversionFi: if (all(dEq0(invFi_current))) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> failed on inversion of current Fi at el ip ipc ',& el,ip,ipc if (iand(debug_level(debug_crystallite), debug_levelExtensive) > 0_pInt) & write(6,'(/,a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> current Fi ', & transpose(crystallite_subFi0(1:3,1:3,ipc,ip,el)) #endif return endif failedInversionFi !* start Li loop with normal step length NiterationStressLi = 0_pInt jacoCounterLi = 0_pInt steplengthLi = 1.0_pReal residuumLi_old = 0.0_pReal LiLoop: do NiterationStressLi = NiterationStressLi + 1_pInt LiLoopLimit: if (NiterationStressLi > nStress) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i3,a,i8,1x,i2,1x,i3,/)') '<< CRYST integrateStress >> reached Li loop limit',nStress, & ' at el ip ipc ', el,ip,ipc #endif return endif LiLoopLimit invFi_new = math_mul33x33(invFi_current,math_I3 - dt*Liguess) Fi_new = math_inv33(invFi_new) detInvFi = math_det33(invFi_new) !* start Lp loop with normal step length NiterationStressLp = 0_pInt jacoCounterLp = 0_pInt steplengthLp = 1.0_pReal residuumLp_old = 0.0_pReal Lpguess_old = Lpguess LpLoop: do NiterationStressLp = NiterationStressLp + 1_pInt LpLoopLimit: if (NiterationStressLp > nStress) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i3,a,i8,1x,i2,1x,i3,/)') '<< CRYST integrateStress >> reached Lp loop limit',nStress, & ' at el ip ipc ', el,ip,ipc #endif return endif LpLoopLimit !* calculate (elastic) 2nd Piola--Kirchhoff stress tensor and its tangent from constitutive law B = math_I3 - dt*Lpguess Fe = math_mul33x33(math_mul33x33(A,B), invFi_new) call constitutive_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi_new, ipc, ip, el) ! call constitutive law to calculate 2nd Piola-Kirchhoff stress and its derivative in unloaded configuration !* calculate plastic velocity gradient and its tangent from constitutive law call constitutive_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, & S, Fi_new, ipc, ip, el) #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,i3,/)') '<< CRYST integrateStress >> iteration ', NiterationStressLp write(6,'(a,/,3(12x,3(e20.10,1x)/))') '<< CRYST integrateStress >> Lpguess', transpose(Lpguess) write(6,'(a,/,3(12x,3(e20.10,1x)/))') '<< CRYST integrateStress >> Lp_constitutive', transpose(Lp_constitutive) write(6,'(a,/,3(12x,3(e20.10,1x)/))') '<< CRYST integrateStress >> Fi', transpose(Fi_new) write(6,'(a,/,3(12x,3(e20.10,1x)/))') '<< CRYST integrateStress >> Fe', transpose(Fe) write(6,'(a,/,3(12x,3(e20.10,1x)/))') '<< CRYST integrateStress >> S', transpose(S) endif #endif !* update current residuum and check for convergence of loop aTolLp = max(rTol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error aTol_crystalliteStress) ! minimum lower cutoff residuumLp = Lpguess - Lp_constitutive if (any(IEEE_is_NaN(residuumLp))) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i8,1x,i2,1x,i3,a,i3,a)') '<< CRYST integrateStress >> encountered NaN for Lp-residuum at el ip ipc ', & el,ip,ipc, & ' ; iteration ', NiterationStressLp,& ' >> returning..!' #endif return ! ...me = .false. to inform integrator about problem elseif (norm2(residuumLp) < aTolLp) then ! converged if below absolute tolerance exit LpLoop ! ...leave iteration loop elseif ( NiterationStressLp == 1_pInt & .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLp_old = residuumLp ! ...remember old values and... Lpguess_old = Lpguess steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLp = subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction Lpguess = Lpguess_old + steplengthLp * deltaLp #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,1x,f7.4)') '<< CRYST integrateStress >> linear search for Lpguess with step', steplengthLp endif #endif cycle LpLoop endif !* calculate Jacobian for correction term if (mod(jacoCounterLp, iJacoLpresiduum) == 0_pInt) then forall(o=1_pInt:3_pInt,p=1_pInt:3_pInt) dFe_dLp(o,1:3,p,1:3) = A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) dFe_dLp = - dt * dFe_dLp dRLp_dLp = math_identity2nd(9_pInt) & - math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp)) #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,/,9(12x,9(e12.4,1x)/))') '<< CRYST integrateStress >> dLp_dS', math_3333to99(dLp_dS) write(6,'(a,1x,e20.10)') '<< CRYST integrateStress >> dLp_dS norm', norm2(math_3333to99(dLp_dS)) write(6,'(a,/,9(12x,9(e12.4,1x)/))') '<< CRYST integrateStress >> dRLp_dLp', dRLp_dLp-math_identity2nd(9_pInt) write(6,'(a,1x,e20.10)') '<< CRYST integrateStress >> dRLp_dLp norm', norm2(dRLp_dLp-math_identity2nd(9_pInt)) endif #endif dRLp_dLp2 = dRLp_dLp ! will be overwritten in first call to LAPACK routine work = math_33to9(residuumLp) call dgesv(9,1,dRLp_dLp2,9,devNull,work,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp if (ierr /= 0_pInt) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) then write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> failed on dR/dLp inversion at el ip ipc ', & el,ip,ipc if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g)& .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,*) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dR_dLp',transpose(dRLp_dLp) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dFe_dLp',transpose(math_3333to99(dFe_dLp)) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dS_dFe (cnst)',transpose(math_3333to99(dS_dFe)) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dLp_dS (cnst)',transpose(math_3333to99(dLp_dS)) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> A',transpose(A) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> B',transpose(B) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Lp_constitutive',transpose(Lp_constitutive) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Lpguess',transpose(Lpguess) endif endif #endif return endif deltaLp = - math_9to33(work) endif jacoCounterLp = jacoCounterLp + 1_pInt Lpguess = Lpguess + steplengthLp * deltaLp enddo LpLoop !* calculate intermediate velocity gradient and its tangent from constitutive law call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, & S, Fi_new, ipc, ip, el) #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Li_constitutive', transpose(Li_constitutive) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Liguess', transpose(Liguess) endif #endif !* update current residuum and check for convergence of loop aTolLi = max(rTol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error aTol_crystalliteStress) ! minimum lower cutoff residuumLi = Liguess - Li_constitutive if (any(IEEE_is_NaN(residuumLi))) then ! NaN in residuum... #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) & write(6,'(a,i8,1x,i2,1x,i3,a,i3,a)') '<< CRYST integrateStress >> encountered NaN for Li-residuum at el ip ipc ', & el,ip,ipc, & ' ; iteration ', NiterationStressLi,& ' >> returning..!' #endif return ! ...me = .false. to inform integrator about problem elseif (norm2(residuumLi) < aTolLi) then ! converged if below absolute tolerance exit LiLoop ! ...leave iteration loop elseif ( NiterationStressLi == 1_pInt & .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLi_old = residuumLi ! ...remember old values and... Liguess_old = Liguess steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLi = subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction Liguess = Liguess_old + steplengthLi * deltaLi cycle LiLoop endif !* calculate Jacobian for correction term if (mod(jacoCounterLi, iJacoLpresiduum) == 0_pInt) then temp_33 = math_mul33x33(math_mul33x33(A,B),invFi_current) forall(o=1_pInt:3_pInt,p=1_pInt:3_pInt) dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current end forall forall(o=1_pInt:3_pInt,p=1_pInt:3_pInt) & dFi_dLi(1:3,1:3,o,p) = math_mul33x33(math_mul33x33(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new) dRLi_dLi = math_identity2nd(9_pInt) & - math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) + & math_mul3333xx3333(dS_dFi, dFi_dLi))) & - math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi)) work = math_33to9(residuumLi) call dgesv(9,1,dRLi_dLi,9,devNull,work,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li if (ierr /= 0_pInt) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) then write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> failed on dR/dLi inversion at el ip ipc ', & el,ip,ipc if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g)& .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,*) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dR_dLi',transpose(dRLi_dLi) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dFe_dLi',transpose(math_3333to99(dFe_dLi)) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dS_dFi (cnst)',transpose(math_3333to99(dS_dFi)) write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST integrateStress >> dLi_dS (cnst)',transpose(math_3333to99(dLi_dS)) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Li_constitutive',transpose(Li_constitutive) write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST integrateStress >> Liguess',transpose(Liguess) endif endif #endif return endif deltaLi = - math_9to33(work) endif jacoCounterLi = jacoCounterLi + 1_pInt Liguess = Liguess + steplengthLi * deltaLi enddo LiLoop !* calculate new plastic and elastic deformation gradient invFp_new = math_mul33x33(invFp_current,B) invFp_new = invFp_new / math_det33(invFp_new)**(1.0_pReal/3.0_pReal) ! regularize Fp_new = math_inv33(invFp_new) failedInversionInvFp: if (all(dEq0(Fp_new))) then #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelBasic) /= 0_pInt) then write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST integrateStress >> failed on invFp_new inversion at el ip ipc ', & el,ip,ipc if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) & write(6,'(/,a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> invFp_new',transpose(invFp_new) endif #endif return endif failedInversionInvFp Fe_new = math_mul33x33(math_mul33x33(Fg_new,invFp_new),invFi_new) !-------------------------------------------------------------------------------------------------- ! stress integration was successful integrateStress = .true. crystallite_P (1:3,1:3,ipc,ip,el) = math_mul33x33(math_mul33x33(Fg_new,invFp_new), & math_mul33x33(S,transpose(invFp_new))) crystallite_S (1:3,1:3,ipc,ip,el) = S crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess crystallite_Li (1:3,1:3,ipc,ip,el) = Liguess crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new crystallite_Fi (1:3,1:3,ipc,ip,el) = Fi_new crystallite_Fe (1:3,1:3,ipc,ip,el) = Fe_new crystallite_invFp(1:3,1:3,ipc,ip,el) = invFp_new crystallite_invFi(1:3,1:3,ipc,ip,el) = invFi_new #ifdef DEBUG if (iand(debug_level(debug_crystallite),debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,/)') '<< CRYST integrateStress >> successful integration' write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> P / MPa', & transpose(crystallite_P(1:3,1:3,ipc,ip,el))*1.0e-6_pReal write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> Cauchy / MPa', & math_mul33x33(crystallite_P(1:3,1:3,ipc,ip,el), transpose(Fg_new)) * 1.0e-6_pReal / math_det33(Fg_new) write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> Fe Lp Fe^-1', & transpose(math_mul33x33(Fe_new, math_mul33x33(crystallite_Lp(1:3,1:3,ipc,ip,el), math_inv33(Fe_new)))) write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> Fp',transpose(crystallite_Fp(1:3,1:3,ipc,ip,el)) write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST integrateStress >> Fi',transpose(crystallite_Fi(1:3,1:3,ipc,ip,el)) endif #endif end function integrateStress !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with adaptive 1st order explicit Euler method !> using Fixed Point Iteration to adapt the stepsize !-------------------------------------------------------------------------------------------------- subroutine integrateStateFPI() #ifdef DEBUG use debug, only: debug_level, & debug_e, & debug_i, & debug_g, & debug_crystallite, & debug_levelBasic, & debug_levelExtensive, & debug_levelSelective #endif use numerics, only: & nState use mesh, only: & mesh_element use material, only: & plasticState, & sourceState, & phaseAt, phasememberAt, & phase_Nsources, & homogenization_Ngrains use constitutive, only: & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizeDotState implicit none integer(pInt) :: & NiterationState, & !< number of iterations in state loop e, & !< element index in element loop i, & !< integration point index in ip loop g, & !< grain index in grain loop p, & c, & s, & sizeDotState real(pReal) :: & zeta real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: & residuum_plastic ! residuum for plastic state real(pReal), dimension(constitutive_source_maxSizeDotState) :: & residuum_source ! residuum for source state logical :: & doneWithIntegration ! --+>> PREGUESS FOR STATE <<+-- call update_dotState(1.0_pReal) call update_state(1.0_pReal) NiterationState = 0_pInt doneWithIntegration = .false. crystalliteLooping: do while (.not. doneWithIntegration .and. NiterationState < nState) NiterationState = NiterationState + 1_pInt #ifdef DEBUG if (iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt) & write(6,'(a,i6)') '<< CRYST stateFPI >> state iteration ',NiterationState #endif ! store previousDotState and previousDotState2 !$OMP PARALLEL DO PRIVATE(p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) plasticState(p)%previousDotState2(:,c) = merge(plasticState(p)%previousDotState(:,c),& 0.0_pReal,& NiterationState > 1_pInt) plasticState(p)%previousDotState (:,c) = plasticState(p)%dotState(:,c) do s = 1_pInt, phase_Nsources(p) sourceState(p)%p(s)%previousDotState2(:,c) = merge(sourceState(p)%p(s)%previousDotState(:,c),& 0.0_pReal, & NiterationState > 1_pInt) sourceState(p)%p(s)%previousDotState (:,c) = sourceState(p)%p(s)%dotState(:,c) enddo endif enddo enddo enddo !$OMP END PARALLEL DO call update_dependentState call update_stress(1.0_pReal) call update_dotState(1.0_pReal) !$OMP PARALLEL !$OMP DO PRIVATE(sizeDotState,residuum_plastic,residuum_source,zeta,p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) sizeDotState = plasticState(p)%sizeDotState zeta = damper(plasticState(p)%dotState (:,c), & plasticState(p)%previousDotState (:,c), & plasticState(p)%previousDotState2(:,c)) residuum_plastic(1:SizeDotState) = plasticState(p)%state (1:sizeDotState,c) & - plasticState(p)%subState0(1:sizeDotState,c) & - ( plasticState(p)%dotState (:,c) * zeta & + plasticState(p)%previousDotState(:,c) * (1.0_pReal-zeta) & ) * crystallite_subdt(g,i,e) plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%state(1:sizeDotState,c) & - residuum_plastic(1:sizeDotState) plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta & + plasticState(p)%previousDotState(:,c) * (1.0_pReal - zeta) crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%aTolState(1:sizeDotState)) do s = 1_pInt, phase_Nsources(p) sizeDotState = sourceState(p)%p(s)%sizeDotState zeta = damper(sourceState(p)%p(s)%dotState (:,c), & sourceState(p)%p(s)%previousDotState (:,c), & sourceState(p)%p(s)%previousDotState2(:,c)) residuum_source(1:sizeDotState) = sourceState(p)%p(s)%state (1:sizeDotState,c) & - sourceState(p)%p(s)%subState0(1:sizeDotState,c) & - ( sourceState(p)%p(s)%dotState (:,c) * zeta & + sourceState(p)%p(s)%previousDotState(:,c) * (1.0_pReal - zeta) & ) * crystallite_subdt(g,i,e) sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%state(1:sizeDotState,c) & - residuum_source(1:sizeDotState) sourceState(p)%p(s)%dotState(:,c) = sourceState(p)%p(s)%dotState(:,c) * zeta & + sourceState(p)%p(s)%previousDotState(:,c)* (1.0_pReal - zeta) crystallite_converged(g,i,e) = & crystallite_converged(g,i,e) .and. converged(residuum_source(1:sizeDotState), & sourceState(p)%p(s)%state(1:sizeDotState,c), & sourceState(p)%p(s)%aTolState(1:sizeDotState)) enddo endif enddo; enddo; enddo !$OMP ENDDO !$OMP DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) !$OMP FLUSH(crystallite_todo) if (crystallite_todo(g,i,e) .and. crystallite_converged(g,i,e)) then ! converged and still alive... crystallite_todo(g,i,e) = stateJump(g,i,e) !$OMP FLUSH(crystallite_todo) if (.not. crystallite_todo(g,i,e)) then ! if state jump fails, then convergence is broken crystallite_converged(g,i,e) = .false. if (.not. crystallite_localPlasticity(g,i,e)) then ! if broken non-local... !$OMP CRITICAL (checkTodo) crystallite_todo = crystallite_todo .and. crystallite_localPlasticity ! ...all non-locals skipped !$OMP END CRITICAL (checkTodo) endif endif endif enddo; enddo; enddo !$OMP ENDDO !$OMP END PARALLEL if (any(plasticState(:)%nonlocal)) call nonlocalConvergenceCheck ! --- CHECK IF DONE WITH INTEGRATION --- doneWithIntegration = .true. do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) then doneWithIntegration = .false. exit endif enddo; enddo enddo enddo crystalliteLooping contains !-------------------------------------------------------------------------------------------------- !> @brief calculate the damping for correction of state and dot state !-------------------------------------------------------------------------------------------------- real(pReal) pure function damper(current,previous,previous2) implicit none real(pReal), dimension(:), intent(in) ::& current, previous, previous2 real(pReal) :: dot_prod12, dot_prod22 dot_prod12 = dot_product(current - previous, previous - previous2) dot_prod22 = dot_product(previous - previous2, previous - previous2) if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22) else damper = 1.0_pReal endif end function damper end subroutine integrateStateFPI !-------------------------------------------------------------------------------------------------- !> @brief integrate state with 1st order explicit Euler method !-------------------------------------------------------------------------------------------------- subroutine integrateStateEuler() use material, only: & plasticState implicit none call update_dotState(1.0_pReal) call update_state(1.0_pReal) call update_deltaState call update_dependentState call update_stress(1.0_pReal) call setConvergenceFlag if (any(plasticState(:)%nonlocal)) call nonlocalConvergenceCheck end subroutine integrateStateEuler !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 1st order Euler method with adaptive step size !-------------------------------------------------------------------------------------------------- subroutine integrateStateAdaptiveEuler() use mesh, only: & theMesh, & mesh_element use material, only: & homogenization_Ngrains, & plasticState, & sourceState, & phaseAt, phasememberAt, & phase_Nsources, & homogenization_maxNgrains use constitutive, only: & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizeDotState implicit none integer(pInt) :: & e, & ! element index in element loop i, & ! integration point index in ip loop g, & ! grain index in grain loop p, & c, & s, & sizeDotState ! ToDo: MD: once all constitutives use allocate state, attach residuum arrays to the state in case of adaptive Euler real(pReal), dimension(constitutive_plasticity_maxSizeDotState, & homogenization_maxNgrains,theMesh%elem%nIPs,theMesh%Nelems) :: & residuum_plastic real(pReal), dimension(constitutive_source_maxSizeDotState,& maxval(phase_Nsources), & homogenization_maxNgrains,theMesh%elem%nIPs,theMesh%Nelems) :: & residuum_source !-------------------------------------------------------------------------------------------------- ! contribution to state and relative residui and from Euler integration call update_dotState(1.0_pReal) !$OMP PARALLEL DO PRIVATE(sizeDotState,p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) sizeDotState = plasticState(p)%sizeDotState residuum_plastic(1:sizeDotState,g,i,e) = plasticState(p)%dotstate(1:sizeDotState,c) & * (- 0.5_pReal * crystallite_subdt(g,i,e)) plasticState(p)%state(1:sizeDotState,c) = & plasticState(p)%state(1:sizeDotState,c) + plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e) !ToDo: state, partitioned state? do s = 1_pInt, phase_Nsources(p) sizeDotState = sourceState(p)%p(s)%sizeDotState residuum_source(1:sizeDotState,s,g,i,e) = sourceState(p)%p(s)%dotstate(1:sizeDotState,c) & * (- 0.5_pReal * crystallite_subdt(g,i,e)) sourceState(p)%p(s)%state(1:sizeDotState,c) = & sourceState(p)%p(s)%state(1:sizeDotState,c) + sourceState(p)%p(s)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e) !ToDo: state, partitioned state? enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO call update_deltaState call update_dependentState call update_stress(1.0_pReal) call update_dotState(1.0_pReal) !$OMP PARALLEL DO PRIVATE(sizeDotState,p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) sizeDotState = plasticState(p)%sizeDotState residuum_plastic(1:sizeDotState,g,i,e) = residuum_plastic(1:sizeDotState,g,i,e) & + 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e) crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState,g,i,e), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%aTolState(1:sizeDotState)) do s = 1_pInt, phase_Nsources(p) sizeDotState = sourceState(p)%p(s)%sizeDotState residuum_source(1:sizeDotState,s,g,i,e) = & residuum_source(1:sizeDotState,s,g,i,e) + 0.5_pReal * sourceState(p)%p(s)%dotState(:,c) * crystallite_subdt(g,i,e) crystallite_converged(g,i,e) = & crystallite_converged(g,i,e) .and. converged(residuum_source(1:sizeDotState,s,g,i,e), & sourceState(p)%p(s)%state(1:sizeDotState,c), & sourceState(p)%p(s)%aTolState(1:sizeDotState)) enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO if (any(plasticState(:)%nonlocal)) call nonlocalConvergenceCheck end subroutine integrateStateAdaptiveEuler !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 4th order explicit Runge Kutta method ! ToDo: This is totally BROKEN: RK4dotState is never used!!! !-------------------------------------------------------------------------------------------------- subroutine integrateStateRK4() use mesh, only: & mesh_element use material, only: & homogenization_Ngrains, & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt implicit none real(pReal), dimension(4), parameter :: & TIMESTEPFRACTION = [0.5_pReal, 0.5_pReal, 1.0_pReal, 1.0_pReal] ! factor giving the fraction of the original timestep used for Runge Kutta Integration real(pReal), dimension(4), parameter :: & WEIGHT = [1.0_pReal, 2.0_pReal, 2.0_pReal, 1.0_pReal/6.0_pReal] ! weight of slope used for Runge Kutta integration (final weight divided by 6) integer(pInt) :: e, & ! element index in element loop i, & ! integration point index in ip loop g, & ! grain index in grain loop p, & ! phase loop c, & n, & s call update_dotState(1.0_pReal) do n = 1_pInt,4_pInt !$OMP PARALLEL DO PRIVATE(p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) plasticState(p)%RK4dotState(:,c) = WEIGHT(n)*plasticState(p)%dotState(:,c) & + merge(plasticState(p)%RK4dotState(:,c),0.0_pReal,n>1_pInt) do s = 1_pInt, phase_Nsources(p) sourceState(p)%p(s)%RK4dotState(:,c) = WEIGHT(n)*sourceState(p)%p(s)%dotState(:,c) & + merge(sourceState(p)%p(s)%RK4dotState(:,c),0.0_pReal,n>1_pInt) enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO call update_state(TIMESTEPFRACTION(n)) call update_deltaState call update_dependentState call update_stress(TIMESTEPFRACTION(n)) ! --- dot state and RK dot state--- first3steps: if (n < 4) then call update_dotState(TIMESTEPFRACTION(n)) endif first3steps enddo call setConvergenceFlag if (any(plasticState(:)%nonlocal)) call nonlocalConvergenceCheck end subroutine integrateStateRK4 !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 5th order Runge-Kutta Cash-Karp method with !> adaptive step size (use 5th order solution to advance = "local extrapolation") !-------------------------------------------------------------------------------------------------- subroutine integrateStateRKCK45() use mesh, only: & mesh_element, & theMesh use material, only: & homogenization_Ngrains, & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt, & homogenization_maxNgrains use constitutive, only: & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizeDotState implicit none real(pReal), dimension(5,5), parameter :: & A = reshape([& .2_pReal, .075_pReal, .3_pReal, -11.0_pReal/54.0_pReal, 1631.0_pReal/55296.0_pReal, & .0_pReal, .225_pReal, -.9_pReal, 2.5_pReal, 175.0_pReal/512.0_pReal, & .0_pReal, .0_pReal, 1.2_pReal, -70.0_pReal/27.0_pReal, 575.0_pReal/13824.0_pReal, & .0_pReal, .0_pReal, .0_pReal, 35.0_pReal/27.0_pReal, 44275.0_pReal/110592.0_pReal, & .0_pReal, .0_pReal, .0_pReal, .0_pReal, 253.0_pReal/4096.0_pReal], & [5,5], order=[2,1]) !< coefficients in Butcher tableau (used for preliminary integration in stages 2 to 6) real(pReal), dimension(6), parameter :: & B = & [37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, & 125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], & !< coefficients in Butcher tableau (used for final integration and error estimate) DB = B - & [2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,& 13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 0.25_pReal] !< coefficients in Butcher tableau (used for final integration and error estimate) real(pReal), dimension(5), parameter :: & C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal] !< coefficients in Butcher tableau (fractions of original time step in stages 2 to 6) integer(pInt) :: & e, & ! element index in element loop i, & ! integration point index in ip loop g, & ! grain index in grain loop stage, & ! stage index in integration stage loop n, & p, & cc, & s, & sizeDotState ! ToDo: MD: once all constitutives use allocate state, attach residuum arrays to the state in case of RKCK45 real(pReal), dimension(constitutive_plasticity_maxSizeDotState, & homogenization_maxNgrains,theMesh%elem%nIPs,theMesh%Nelems) :: & residuum_plastic ! relative residuum from evolution in microstructure real(pReal), dimension(constitutive_source_maxSizeDotState, & maxval(phase_Nsources), & homogenization_maxNgrains,theMesh%elem%nIPs,theMesh%Nelems) :: & residuum_source ! relative residuum from evolution in microstructure call update_dotState(1.0_pReal) ! --- SECOND TO SIXTH RUNGE KUTTA STEP --- do stage = 1_pInt,5_pInt ! --- state update --- !$OMP PARALLEL DO PRIVATE(p,cc) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); cc = phasememberAt(g,i,e) plasticState(p)%RKCK45dotState(stage,:,cc) = plasticState(p)%dotState(:,cc) plasticState(p)%dotState(:,cc) = A(1,stage) * plasticState(p)%RKCK45dotState(1,:,cc) do s = 1_pInt, phase_Nsources(p) sourceState(p)%p(s)%RKCK45dotState(stage,:,cc) = sourceState(p)%p(s)%dotState(:,cc) sourceState(p)%p(s)%dotState(:,cc) = A(1,stage) * sourceState(p)%p(s)%RKCK45dotState(1,:,cc) enddo do n = 2_pInt, stage plasticState(p)%dotState(:,cc) = plasticState(p)%dotState(:,cc) & + A(n,stage) * plasticState(p)%RKCK45dotState(n,:,cc) do s = 1_pInt, phase_Nsources(p) sourceState(p)%p(s)%dotState(:,cc) = sourceState(p)%p(s)%dotState(:,cc) & + A(n,stage) * sourceState(p)%p(s)%RKCK45dotState(n,:,cc) enddo enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO call update_state(1.0_pReal) !MD: 1.0 correct? call update_deltaState call update_dependentState call update_stress(C(stage)) call update_dotState(C(stage)) enddo !-------------------------------------------------------------------------------------------------- ! --- STATE UPDATE WITH ERROR ESTIMATE FOR STATE --- !$OMP PARALLEL DO PRIVATE(sizeDotState,p,cc) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); cc = phasememberAt(g,i,e) sizeDotState = plasticState(p)%sizeDotState plasticState(p)%RKCK45dotState(6,:,cc) = plasticState (p)%dotState(:,cc) residuum_plastic(1:sizeDotState,g,i,e) = & matmul(transpose(plasticState(p)%RKCK45dotState(1:6,1:sizeDotState,cc)),DB) & ! why transpose? Better to transpose constant DB * crystallite_subdt(g,i,e) plasticState(p)%dotState(:,cc) = & matmul(transpose(plasticState(p)%RKCK45dotState(1:6,1:sizeDotState,cc)), B) ! why transpose? Better to transpose constant B do s = 1_pInt, phase_Nsources(p) sizeDotState = sourceState(p)%p(s)%sizeDotState sourceState(p)%p(s)%RKCK45dotState(6,:,cc) = sourceState(p)%p(s)%dotState(:,cc) residuum_source(1:sizeDotState,s,g,i,e) = & matmul(transpose(sourceState(p)%p(s)%RKCK45dotState(1:6,1:sizeDotState,cc)),DB) & * crystallite_subdt(g,i,e) sourceState(p)%p(s)%dotState(:,cc) = & matmul(transpose(sourceState(p)%p(s)%RKCK45dotState(1:6,1:sizeDotState,cc)),B) enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO call update_state(1.0_pReal) ! --- relative residui and state convergence --- !$OMP PARALLEL DO PRIVATE(sizeDotState,p,cc) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e)) then p = phaseAt(g,i,e); cc = phasememberAt(g,i,e) sizeDotState = plasticState(p)%sizeDotState crystallite_todo(g,i,e) = converged(residuum_plastic(1:sizeDotState,g,i,e), & plasticState(p)%state(1:sizeDotState,cc), & plasticState(p)%aTolState(1:sizeDotState)) do s = 1_pInt, phase_Nsources(p) sizeDotState = sourceState(p)%p(s)%sizeDotState crystallite_todo(g,i,e) = & crystallite_todo(g,i,e) .and. converged(residuum_source(1:sizeDotState,s,g,i,e), & sourceState(p)%p(s)%state(1:sizeDotState,cc), & sourceState(p)%p(s)%aTolState(1:sizeDotState)) enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO call update_deltaState call update_dependentState call update_stress(1.0_pReal) call setConvergenceFlag if (any(plasticState(:)%nonlocal)) call nonlocalConvergenceCheck end subroutine integrateStateRKCK45 !-------------------------------------------------------------------------------------------------- !> @brief sets convergence flag for nonlocal calculations !> @detail one non-converged nonlocal sets all other nonlocals to non-converged to trigger cut back !-------------------------------------------------------------------------------------------------- subroutine nonlocalConvergenceCheck() implicit none if (any(.not. crystallite_converged .and. .not. crystallite_localPlasticity)) & ! any non-local not yet converged (or broken)... where( .not. crystallite_localPlasticity) crystallite_converged = .false. end subroutine nonlocalConvergenceCheck !-------------------------------------------------------------------------------------------------- !> @brief Sets convergence flag based on "todo": every point that survived the integration (todo is ! still .true. is considered as converged !> @details: For explicitEuler, RK4 and RKCK45, adaptive Euler and FPI have their on criteria !-------------------------------------------------------------------------------------------------- subroutine setConvergenceFlag() use mesh, only: & mesh_element implicit none integer(pInt) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop !OMP DO PARALLEL PRIVATE(i,g) do e = FEsolving_execElem(1),FEsolving_execElem(2) forall (i = FEsolving_execIP(1,e):FEsolving_execIP(2,e), & g = 1:homogenization_Ngrains(mesh_element(3,e))) crystallite_converged(g,i,e) = crystallite_todo(g,i,e) .or. crystallite_converged(g,i,e) ! if still "to do" then converged per definition end forall; enddo !OMP END DO PARALLEL end subroutine setConvergenceFlag !-------------------------------------------------------------------------------------------------- !> @brief determines whether a point is converged !-------------------------------------------------------------------------------------------------- logical pure function converged(residuum,state,aTol) use prec, only: & dEq0 use numerics, only: & rTol => rTol_crystalliteState implicit none real(pReal), intent(in), dimension(:) ::& residuum, state, aTol converged = all(abs(residuum) <= max(aTol, rTol*abs(state))) end function converged !-------------------------------------------------------------------------------------------------- !> @brief Standard forwarding of state as state = state0 + dotState * (delta t) !-------------------------------------------------------------------------------------------------- subroutine update_stress(timeFraction) use mesh, only: & mesh_element implicit none real(pReal), intent(in) :: & timeFraction integer(pInt) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) !$OMP FLUSH(crystallite_todo) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) then crystallite_todo(g,i,e) = integrateStress(g,i,e,timeFraction) !$OMP FLUSH(crystallite_todo) if (.not. crystallite_todo(g,i,e) .and. .not. crystallite_localPlasticity(g,i,e)) then ! if broken non-local... !$OMP CRITICAL (checkTodo) crystallite_todo = crystallite_todo .and. crystallite_localPlasticity ! ...all non-locals skipped !$OMP END CRITICAL (checkTodo) endif endif enddo; enddo; enddo !$OMP END PARALLEL DO end subroutine update_stress !-------------------------------------------------------------------------------------------------- !> @brief tbd !-------------------------------------------------------------------------------------------------- subroutine update_dependentState() use mesh, only: & mesh_element use constitutive, only: & constitutive_dependentState => constitutive_microstructure implicit none integer(pInt) :: e, & ! element index in element loop i, & ! integration point index in ip loop g ! grain index in grain loop !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) & call constitutive_dependentState(crystallite_Fe(1:3,1:3,g,i,e), & crystallite_Fp(1:3,1:3,g,i,e), & g, i, e) enddo; enddo; enddo !$OMP END PARALLEL DO end subroutine update_dependentState !-------------------------------------------------------------------------------------------------- !> @brief Standard forwarding of state as state = state0 + dotState * (delta t) !-------------------------------------------------------------------------------------------------- subroutine update_state(timeFraction) use material, only: & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt use mesh, only: & mesh_element implicit none real(pReal), intent(in) :: & timeFraction integer(pInt) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g, & !< grain index in grain loop p, & c, & s, & mySize !$OMP PARALLEL DO PRIVATE(mySize,p,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) if (crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) then p = phaseAt(g,i,e); c = phasememberAt(g,i,e) mySize = plasticState(p)%sizeDotState plasticState(p)%state(1:mySize,c) = plasticState(p)%subState0(1:mySize,c) & + plasticState(p)%dotState (1:mySize,c) & * crystallite_subdt(g,i,e) * timeFraction do s = 1_pInt, phase_Nsources(p) mySize = sourceState(p)%p(s)%sizeDotState sourceState(p)%p(s)%state(1:mySize,c) = sourceState(p)%p(s)%subState0(1:mySize,c) & + sourceState(p)%p(s)%dotState (1:mySize,c) & * crystallite_subdt(g,i,e) * timeFraction enddo endif enddo; enddo; enddo !$OMP END PARALLEL DO end subroutine update_state !-------------------------------------------------------------------------------------------------- !> @brief triggers calculation of all new rates !> if NaN occurs, crystallite_todo is set to FALSE. Any NaN in a nonlocal propagates to all others !-------------------------------------------------------------------------------------------------- subroutine update_dotState(timeFraction) use, intrinsic :: & IEEE_arithmetic use material, only: & plasticState, & sourceState, & phaseAt, phasememberAt, & phase_Nsources use mesh, only: & mesh_element use constitutive, only: & constitutive_collectDotState implicit none real(pReal), intent(in) :: & timeFraction integer(pInt) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g, & !< grain index in grain loop p, & c, & s logical :: & NaN, & nonlocalStop nonlocalStop = .false. !$OMP PARALLEL DO PRIVATE (p,c,NaN) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) !$OMP FLUSH(nonlocalStop) if ((crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) .and. .not. nonlocalStop) then call constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fe, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_Fp, & crystallite_subdt(g,i,e)*timeFraction, g,i,e) p = phaseAt(g,i,e); c = phasememberAt(g,i,e) NaN = any(IEEE_is_NaN(plasticState(p)%dotState(:,c))) do s = 1_pInt, phase_Nsources(p) NaN = NaN .or. any(IEEE_is_NaN(sourceState(p)%p(s)%dotState(:,c))) enddo if (NaN) then crystallite_todo(g,i,e) = .false. ! this one done (and broken) if (.not. crystallite_localPlasticity(g,i,e)) nonlocalStop = .True. endif endif enddo; enddo; enddo !$OMP END PARALLEL DO if (nonlocalStop) crystallite_todo = crystallite_todo .and. crystallite_localPlasticity end subroutine update_DotState subroutine update_deltaState use, intrinsic :: & IEEE_arithmetic use prec, only: & dNeq0 use mesh, only: & mesh_element use material, only: & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt use constitutive, only: & constitutive_collectDeltaState implicit none integer(pInt) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g, & !< grain index in grain loop p, & mySize, & myOffset, & c, & s logical :: & NaN, & nonlocalStop nonlocalStop = .false. !$OMP PARALLEL DO PRIVATE(p,c,myOffset,mySize,NaN) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,homogenization_Ngrains(mesh_element(3,e)) !$OMP FLUSH(nonlocalStop) if ((crystallite_todo(g,i,e) .and. .not. crystallite_converged(g,i,e)) .and. .not. nonlocalStop) then call constitutive_collectDeltaState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fe(1:3,1:3,g,i,e), & crystallite_Fi(1:3,1:3,g,i,e), & g,i,e) p = phaseAt(g,i,e); c = phasememberAt(g,i,e) myOffset = plasticState(p)%offsetDeltaState mySize = plasticState(p)%sizeDeltaState NaN = any(IEEE_is_NaN(plasticState(p)%deltaState(1:mySize,c))) if (.not. NaN) then plasticState(p)%state(myOffset + 1_pInt: myOffset + mySize,c) = & plasticState(p)%state(myOffset + 1_pInt: myOffset + mySize,c) + plasticState(p)%deltaState(1:mySize,c) do s = 1_pInt, phase_Nsources(p) myOffset = sourceState(p)%p(s)%offsetDeltaState mySize = sourceState(p)%p(s)%sizeDeltaState NaN = NaN .or. any(IEEE_is_NaN(sourceState(p)%p(s)%deltaState(1:mySize,c))) if (.not. NaN) then sourceState(p)%p(s)%state(myOffset + 1_pInt:myOffset + mySize,c) = & sourceState(p)%p(s)%state(myOffset + 1_pInt:myOffset + mySize,c) + sourceState(p)%p(s)%deltaState(1:mySize,c) endif enddo endif crystallite_todo(g,i,e) = .not. NaN if (.not. crystallite_todo(g,i,e)) then ! if state jump fails, then convergence is broken crystallite_converged(g,i,e) = .false. if (.not. crystallite_localPlasticity(g,i,e)) nonlocalStop = .true. endif endif enddo; enddo; enddo !$OMP END PARALLEL DO if (nonlocalStop) crystallite_todo = crystallite_todo .and. crystallite_localPlasticity end subroutine update_deltaState !-------------------------------------------------------------------------------------------------- !> @brief calculates a jump in the state according to the current state and the current stress !> returns true, if state jump was successfull or not needed. false indicates NaN in delta state !-------------------------------------------------------------------------------------------------- logical function stateJump(ipc,ip,el) use, intrinsic :: & IEEE_arithmetic use prec, only: & dNeq0 #ifdef DEBUG use debug, only: & debug_e, & debug_i, & debug_g, & debug_level, & debug_crystallite, & debug_levelExtensive, & debug_levelSelective #endif use material, only: & plasticState, & sourceState, & phase_Nsources, & phaseAt, phasememberAt use mesh, only: & mesh_element use constitutive, only: & constitutive_collectDeltaState implicit none integer(pInt), intent(in):: & el, & ! element index ip, & ! integration point index ipc ! grain index integer(pInt) :: & c, & p, & mySource, & myOffset, & mySize c = phasememberAt(ipc,ip,el) p = phaseAt(ipc,ip,el) call constitutive_collectDeltaState(crystallite_S(1:3,1:3,ipc,ip,el), & crystallite_Fe(1:3,1:3,ipc,ip,el), & crystallite_Fi(1:3,1:3,ipc,ip,el), & ipc,ip,el) myOffset = plasticState(p)%offsetDeltaState mySize = plasticState(p)%sizeDeltaState if( any(IEEE_is_NaN(plasticState(p)%deltaState(1:mySize,c)))) then ! NaN occured in deltaState stateJump = .false. return endif plasticState(p)%state(myOffset + 1_pInt:myOffset + mySize,c) = & plasticState(p)%state(myOffset + 1_pInt:myOffset + mySize,c) + plasticState(p)%deltaState(1:mySize,c) do mySource = 1_pInt, phase_Nsources(p) myOffset = sourceState(p)%p(mySource)%offsetDeltaState mySize = sourceState(p)%p(mySource)%sizeDeltaState if (any(IEEE_is_NaN(sourceState(p)%p(mySource)%deltaState(1:mySize,c)))) then ! NaN occured in deltaState stateJump = .false. return endif sourceState(p)%p(mySource)%state(myOffset + 1_pInt: myOffset + mySize,c) = & sourceState(p)%p(mySource)%state(myOffset + 1_pInt: myOffset + mySize,c) + sourceState(p)%p(mySource)%deltaState(1:mySize,c) enddo #ifdef DEBUG if (any(dNeq0(plasticState(p)%deltaState(1:mySize,c))) & .and. iand(debug_level(debug_crystallite), debug_levelExtensive) /= 0_pInt & .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) & .or. .not. iand(debug_level(debug_crystallite), debug_levelSelective) /= 0_pInt)) then write(6,'(a,i8,1x,i2,1x,i3, /)') '<< CRYST >> update state at el ip ipc ',el,ip,ipc write(6,'(a,/,(12x,12(e12.5,1x)),/)') '<< CRYST >> deltaState', plasticState(p)%deltaState(1:mySize,c) write(6,'(a,/,(12x,12(e12.5,1x)),/)') '<< CRYST >> new state', & plasticState(p)%state(myOffset + 1_pInt : & myOffset + mySize,c) endif #endif stateJump = .true. end function stateJump end module crystallite