ITASCA公司培训PPT（PFC-basics） 91页

ParticleFlowCode(PFC2D/3D)BasicTrainingCoursePeterCundall,YanhuiHan&RogerHartItascaConsultingGroup,Inc.ItascaSoftwareTrainingCourseTongjiUniversityShanghai,ChinaOctober27-31,2008 PFCBasicTrainingCourseTopic1:PFCFeaturesandTheoreticalBasisFeaturesTheoryTopic2:PFCTutorialCommandsummarySimplePFCdatafileswithoutFISHSetupPFCmodelsinprogressivelycomplexmannerTopic3:FISHdescriptionandtutorialFISHdescriptionImplementball-generationalgorithmImplementwall-basedservo-controlModelingapproachesandFishTankmodelingapproachesmaterialgenesismaterialtestingacompressiontestexample Topic1:PFCFeaturesandTheoreticalBasisFeaturesTheory Modelingofdynamicbehaviorofassembliesofarbitrarily-sizedparticles;particleradiimaydistributeuniformlyoraccordingtoaGaussiandistributionPropertiesareassociatedwithindividualparticles,allowingcontinuousgradationsinpropertiesandparticleradiiDoubleprecisionstorageofparticlecoordinatesandradiiensurelong-termfreedomfromnumericaldriftPFC2D/3DFeatures Contactphysicsconsistsof:linearspringsorsimplifiedHertz-Mindlinlaw,Coulombsliding,andcontactorparallelbondingClumplogicsupportscreationofgroupsofslavedparticlesorclumps;clumpscanserveas“superparticles”ofgeneralshapeAnynumberofarbitrarily-orientedlinesegmentsmaybespecifiedaswalls,eachwithitsowncontactproperties;generalwallsprovidegeometricobjects;assembliesareloadedthroughprescribedwallvelocitiesPFC2D/3DFeatures AutomatictimestepcalculationthatensuresastablesolutionCell-mappingschemetoensurethatsolutiontimeincreaseslinearlywiththenumberofparticlesParticlesandwallsmaybeaddedordeleted(andpropertieschanged)atanytimeduringasimulationTwotypesofdampingavailable:localnonviscousandviscousPFC2D/3DFeatures DensityscalingmaybeusedtoincreasetimestepandoptimizesolutionefficiencyEnergytracingallowsobservationof:bodywork,bondenergy,boundarywork,frictionalwork,kineticenergy,strainenergyMeasurementsofaveragestress,strainrateandporositycanbemadeoveranynumberofspecifiedcircularregionsPFC2D/3DFeatures AnyquantitymaybetracedwithtimeandstoredandplottedasahistoryAquasi-staticoperatingmodeisavailable(inadditiontofullydynamicmode)toensurerapidconvergencetosteadystatesolutionPowerfulbuilt-inprogramminglanguage(FISH)providesfullaccesstointernalstatevariablesandallowsonetocustomizeanalysesPFC2D/3DFeatures Explicitsolutionschemeprovidesastablesolutionforunstablephysicalprocessesandmakesitpossibletosimulatethenon-linearinteractionofalargenumberofparticleswithoutexcessivememoryrequirementsortheneedforaniterativeprocedureBuilt-incontactmodelsinclude:simpleviscoelasticmodel,simpleductilemodel,anddisplacement-softeningmodelPFC2D/3DFeatures PFC(2D&3D)modelstwotypesofobjects:ballsandwallsBallsaredisks(3degreesoffreedom)orspheres(6dof).Also,clumpsarearbitrarilyshapedgroupsofrigidlyattachedballs.Thefullequationsofmotionaresolvedforballs&clumps.Wallsaresurfacesthatcaninteractwithballs(butnotwithotherwalls),andcanbeplanarpolygonsorspecialshapes:spiral,cylinder.Wallsmaymovewithuser-specifiedvelocitiesorspins,orbyprogrammedfunction.Theinteractionsbetweenobjects(ball-ballorball-wall)canbeanyforce/displacementlaw–e.g.,linear,Hertzian(nonlinear),hysteretic,viscous,brittle-bonded,ductile-bonded,etc.PFC2D/3DTheory Contacts–visualization¬ationBall-ballcontactBall-wallcontactPFC2D/3DTheory Unitnormalvector-Distancebetweencentroids-Overlap-Thenormalforceisderiveddirectlyfromtheoverlap:However,theshearforceisderivedincrementally:wheretheincrementalsheardisplacementis:basedontherelativeshearvelocityvector:PFC2D/3DTheory …wheretherelativevelocityvectoratthecontactisgivenby:usingthefollowingnotation:Finally,theshearforceisderived:Andtheparticleforcesandmomentsareobtainedfromthetotalcontactforcevector,givenby-ShearforcevectorcorrectedbycontactspinPFC2D/3DTheory Contactformulations:Thepreviousdevelopmentassumedalinearspringmodelatcontactpoints:(normal)(shear)Thisdefaultmodelalsoallowsslip,duetofriction:IfthenInaddition,thereareanumberofothermodels,bothbuilt-inanduser-defined.TheHertz-Mindlinmodelisanonlinearmodelderivedfromtheanalysisofcontactbetweentwoelasticspheres:NormalsecantstiffnessSheartangentstiffnessPFC2D/3DTheory Therearetwobuilt-inbondingmodels:thecontact-bondandtheparallel-bond.Contact-bondbehaviorisillustratedasfollows.NormaldirectionSheardirectionThecontactbondiseitherintactorbroken.Itmaybebrokenbyeithertheshearorthenormalstrengthbeingexceeded.Ifbroken,thecontactrevertstounbondedbehavior(e.g.,slipispossible).PFC2D/3DTheory Contactbondssimplyassociateastrengthlimittoshearandnormalcontactforces.Nomomentisgenerated.Parallelbondsassumethatbondingisoverafiniteareaofcontact,sothatmomentsmaybegeneratedinresponsetotwistingandbending.DirectforcesMomentsPFC2D/3DTheory Theparallel-bondforcesactinparallelwiththeregularcontactforces(describedearlier),providingextracontactstiffness.Maximumfiberstressesarecalculated,andthebondbrokenifanystresscomponentexceedsthecorrespondingstrength.PFCalsoallowsuser-definedcontactmodels.ThesearecompiledasDLLs(dynamiclinklibraries)andloadedintoPFCasneeded.Examplesofuser-definedmodelsareprovidedwithPFC–e.g.,avisco-elasticmodelandageneralsofteningmodel…PFC2D/3DTheory Thegeneralsofteningmodelprovidesductilepost-peakbehavior,ratherthanthebrittlebehaviorofthedefaultbondingmodels.ForceDisplacementAsingleyieldconditioncombinesbothshearandnormalyield(ratherthanseparateconditions,forthedefaultmodels)…PFC2D/3DTheory ShearforceNormalforceTheyieldenvelope“softens”(contracts)asafunctionofplastic(irreversible)displacement:usinganassociatedflowrule:PFC2D/3DTheory Dampingformulations:PFCmaybeusedtosimulateeitherstaticordynamicsystems.Further,thereareseveraldistinctclassesofproblems(e.g.,impact;free-flight;flow;compactsolid).Thus,severalformsofdampingareavailable.Default,“local”damping–goodforgeneralstaticsolutionofcompactassemblies.Viscouscontactdamping–forsystemsinwhichmanyparticlesareinfreeflight,andthenformstableassemblies.Hystereticcontactdamping–goodformodelingimpactoffragments,butnotprolongedcontact.PFC2D/3DTheory localdamping:Velocity-proportionaldampingintroducesbodyforcesthatcanaffectthesolution.LocaldampingisthedefaultdampinginPFC.Thedampingforceataballisproportionaltothemagnitudeoftheunbalancedforcewiththesignsettoensurethatvibrationalmodesaredamped.PFC2D/3DTheory Dampingforcesareintroducedtotheequationsofmotion:whereistheunbalancedforce.ThedampingforceisTheunbalancedforceratio(averageunbalancedforceoveraveragecontactforce)canbemonitoredtocheckforstaticequilibrium.Whenthisratioislessthanasmallvalue,thenthemodelisconsideredtobeinstaticequilibrium.(SeetheSOLVEcommand.)localdamping:PFC2D/3DTheory Twomainfieldsofapplication:PFChasbeenappliedintwomainfields-SimulationofdeformationandflowofgranularmaterialFractureofbrittleelasticsolidsInbothofthesecasesthe“syntheticmaterial”(consistingofanassemblyofparticles)mustbecalibratedbyperformingsimulatedlaboratorytests.PFC2D/3DTheory Calibration:Normally,testsareperformedtomatchthefollowingpropertiesforrealmaterialsbeforeperformingfullsimulations:ElasticmoduliandPoisson’sratioPeakstrengthOptionally,thefollowingpropertiesmaybematched:SofteningslopeResidualstrengthFracturetoughness(forabrittlesolid)Crackinitiationstress(forabrittlesolid)PFC2D/3DTheory Brittlesolids–relationofPFCmodeltoLEFMconceptsTherelationofanumericalparticlemodeltothebehaviorandpropertiesofagranularmaterialarewell-documented.However,theuseofbonded-particleassembliestorepresentbrittlesolidshashardlybeenjustifiedtheoreticallyintheliterature.Atheoreticallinkbetweenmicro-propertiesandLEFMmechanismsandproperties(fracturetoughness)isderived,asfollows…PFC2D/3DTheory Conclusion:PFCisausefultoolformodelingmaterialwithmicro-structure.ManymechanismsevolvenaturallyinthePFCmodel,comparedtoacontinuummodel,inwhicheacheffectmustbepre-programmed.Aparticlemodelofsoil,rockandconcreteexhibitsemergentproperties–i.e.,themacrobehaviorismorecomplicatedthanthemicrobehavior,andnewmechanismsemerge.PFC2D/3DTheory Topic2:PFCTutorialCommandsummarySimplePFCdatafileswithoutFISHSetupPFCmodelsinprogressivelycomplexmanner CommandSummary(1) CommandSummary(2) CommandSummary(3) CommandSummary(4) RANGElogic(1) RANGElogic(2)Built-inrangeelements:annulus,circle,line,segment,x,ycolor,id,radiusjsetgroupFISHrangeelementsviauser-definedFISHfunction Historylogicsamplesandstoresspecifiedmodelvariablesduringarunbuilt-invariables---e.g.,ballposition,velocityFISHvariables---e.g.,detonationpressurehistoryvariablescanthenbeplottedversusstepnumberorversusotherhistoryvariablesallhistoryvariablesaresampledatasinglesamplinginterval---e.g.,every20steps PlottinglogicSupportsinteractiveviewingandhardcopyMultiple“views”canbedefinedEachviewcontainsalistof“plot-items”Mostplot-itemsaremodifiedbyswitchescolor,id,shade,... MeasurementlogicSupportsautomaticcomputationofcertainquantitiesovercircular/sphericalregions(measurementcirclesormeasurementspheres)Measuredquantitiesinclude:coordinationnumberporosityslidingfractionstressstrainrateFireuptheelectronicmanualTheory&Back.,Section3.4 TwoBallColliding SingleBallFalling SingleBallSlidingAlongConvexCorner SingleBallSlidingIntoConcaveCorner 20BallsFallingintoBox TightPackingof20Balls SimpleBiaxialTest AddContactorParallelBonds Topic3:FISHdescriptionandtutorialFISHdescriptionImplementball-generationalgorithmImplementwall-basedservo-controlIntroduceFishTankmaterialgenesismaterialtestingcompressiontestingexample FISHDescriptionFISH(FLAC-ish)isabuilt-inprogramminglanguageforItascasoftware FISHDescriptionFISH(FLAC-ish)isabuilt-inprogramminglanguageforItascasoftwarefunctionsareenteredviaadatafileandarecompiledintoalistofinstructionsstoredinthecode’smemoryspacevariablesareglobalandareavailableformonitoringorchangingatanytime(viatheSETcommand)dynamicallytyped(integer,float,string,pointer,array)typicalusesofFISHinclude:defineanewcommanddefineanewrangeelement,historyvariableorplotitemcontrolaseriesofrunsmodifythesolutionprocedure(functioniscalledateverytimestep)seenextslideforexample FISHDescriptionHereisaFISHfunctiontodeleteallparticleswithinagivencircle:partofadatafiledefmake_circlebp=ball_headloopwhilebp#nullnext_ball=b_next(bp)dist=sqrt((b_x(bp)-xcen)^2+(b_y(bp)-ycen)^2)ifdist<(rad+b_rad(bp))thenii=b_delete(bp)end_ifbp=next_ballend_loopendSETxcen=5.0,ycen=5.0,rad=2.1make_circledefinenewfunctionsetparametersusenewfunction FISHDescriptionControlStatementsDEFINEfunctionbodyENDCASEOF...END_CASEIF...ELSE...END_IFLOOP...END_LOOPLOOPWHILE...END_LOOPSECTION...END_SECTIONEXITandEXITSECTIONFISHRef.,Sec.2.3.2 FISHDescriptionPFCLinkagesFISHvariablesmaybeprintedorsetfromthePFCcommandlineviathePRINT&SETcommandsPFCcommandsmaybeexecutedfromwithinaFISHfunctionbyenclosingthemwithinCOMMAND...END_COMMANDaFISHsymbolmaybesubstitutedanywhereinaPFCcommandwhereanumberisexpected---e.g.,PROPERTYkn=ball_stiffFISHfunctionsmaybecalledfromseveralplaceswithinthecalculationcycleandwhenparticulareventsoccurduringexecutionviaFISHCALLsFISHRef.,Sec.2.4 FISHDescriptionPredefinedVariablesandFunctionsintrinsicfunctionsmathematical&utilityfunctionstablefunctionsmemory-accessfunctionsplottingfunctionsinput-outputfunctionsPFC-specificfunctionssupportandstandardfunctions(e.g.,linked-listheaders)ballfunctionscontactfunctionswall(&wall-segment)functionsparallel-bondfunctionsmeasurement-circlefunctionsclumpfunctionsFISHRef.,Sec.2.5 ball_headb_nextb_xb_id(15).....b_nextb_xb_id(14).....b_nextb_xb_id(13).....nullb_nextb_xb_id(12)..... TraversingContactsAroundaBall TraversingContactsAroundaBall Example2.11ControllingaseriesofPFC2Druns(fishr12.dat) Ball-generationalgorithmGenerateacollectionofparticlesofauniformsizedistributionwithradiiintherangethatfillagivenarea,A,atagivenporosity,n.Compute:GENERATENballsathalftheirfinalsize.Computeporosity,,ofgeneratedassembly.Multiplyallballradiibyfactorsee3.8.3inFISHinPFC2D Ball-generationalgorithmBall-generationprocess(bg.dvr)generatetheconfiningwallgenerateparticlesathalfoftheirfinalsizes(noparticleoverlap)computecurrentvoidration0expandtheparticlesbym=sqrt(n/n0)Solve/steptoequilibrium Simplewall-basedservo-controlImplementawall-servo(bg1.dvr)includeoperationsinbg.dvrmodifyvelocityofawallsoastomaintainanaverageofwallstressactivateservofunctionfromFISHCALL,everystepkeepadjustingverticalvelocityofthetopwallintheprocessofrunningthesystemintoequilibrium(servocontrol) DirectandIndirectModelingApproachesRockisabrittleheterogeneousmaterialthatexhibitsinelasticdeformationbecauseoftheexistenceandformationofnumerousmicro-cracks.Underincreasingload,thesemicro-crackscoalesceintomacro-cracks,orfractures.Theapproachesformodelingthisinelasticdeformationandfracturecanbeclassifiedintotwocategories,dependingonwhetherdamageisrepresentedindirectlyviaitseffectonconstitutiverelations,ordirectlybytheformationandtrackingofalargenumberofmicro-cracks. DirectandIndirectModelingApproachesMostindirectmodelingapproachesidealizethematerialasacontinuumutilizeaveragemeasuresofmaterialdegradationinconstitutiverelationstorepresentirreversiblemicro-structuraldamagesrelationsbetweenmodelpropertiesandmaterialpropertyknownpropertiesnotaffectedbydiscretizationDirectmodelingapproachesidealizethematerialasacollectionofstructuralunits(springs,beams,etc.)orseparateparticlesbondedtogetherattheircontactpointutilizethebreakageofindividualstructuralunitsorbondstorepresentdamagecalibratemacro-propertiessothatthebehavioroftheresultingsyntheticmaterialresemblesthatofanintendedphysicalmaterialDirectapproacheshavebeenusedtohelpdeveloptheconstitutiverelationsrequiredbyindirectmethodstosolveboundary-valueproblemsIncreasesincomputingpowerhavemadeitfeasibletomodelentireboundary-valueproblemswithdirectapproaches,therebysimulatingthephysicalmicro-mechanismsdirectly Micro-PropertyCalibrationUnbondedcontactmodel-Deformation-Micro-propertyspecification Micro-PropertyCalibrationContact-bondmodelAreaandmomentofinertia-StrengthContactYoung’smodulus-Deformation-Micro-propertyspecification Micro-PropertyCalibrationParallel-bondmodelAreaandmomentofinertia-Strength-Deformation-Micro-propertyspecificationDirectone-to-onecorrespondencebetweenparallel-bondstrengthsandmaterialstrengths. Micro-PropertyCalibrationCalibrateelasticproperties,peakstrengthandcrackinitiationstress FishTank FishTank SpecimenGenesisThematerial-genesisprocedureproducesasyntheticmaterialconsistingofgrains(eithercircular/sphericalparticlesand/orclumps)andcement(contactand/orparallelbonds).Thematerialisproducedinamaterialvesselsuchthatitformsanisotropicandwell-connectedsystemataspecifiedconfiningpressure.Granularmaterialisproducedbynotaddingcementduringthefinalstageoftheprocedure. SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis SpecimenGenesis MaterialTestingSupportTestingconsiderationsStrain-applicationschemeforcompressiontestsStressandstrainmeasurementschemesLoadingrateSupportedmaterial-testscompression(bothconfinedandfullyunconfined)directtensionBraziliantension MaterialTestingSupport MaterialTestingSupport MaterialTestingSupport AMaterialGenesisandCompressionTestingExample AMaterialGenesisandCompressionTestingExampleWecan“develop”ourownFISHfunctions(putallfunctionanddrivefilesinthesamefolderhere)formaterialgenesisandtesting,forexample,runthefollowingdata:C:Itasca_Shanghai2008PFC-trainingexamplesCompTest-3Dcompest-3d.datAlternately,wecanalsotakeadvantageofFishTank,e.g.,callC:Itasca_Shanghai2008PFC-trainingpfc3d_32fist emplatescomptest-3d.dvrSo,FishTankisnothingbutawell-structuredcollection/libraryofgeneral,reusableFISHfunctionsanddrivefilesthatassistmaterialgenesisandtests! AMaterialGenesisandCompressionTestingExample