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MULTISCALEANALYSISOFDEFORMATIONANDFAILUREOFMATERIALSJinghongFanKazuoInamoriSchoolofEngineering,AlfredUniversity,NewYork,USAMULTISCALEANALYSISOFDEFORMATIONANDFAILUREOFMATERIALSMicrosystemandNanotechnologySeriesSeriesEditors–RonaldPethigandHoratioDanteEspinosaFluidPropertiesatNanoMesoScaleDysonetalSeptemberIntroductiontoMicrosystemTechnologyGerlachMarchACElectrokinetics:ColloidsandNanoparticlesMorganGreenJanuaryMicrofluidicTechnologyandApplicationsKochetalNovemberMULTISCALEANALYSISOFDEFORMATIONANDFAILUREOFMATERIALSJinghongFanKazuoInamoriSchoolofEngineering,AlfredUniversity,NewYork,USAThiseditionfirstpublished�,JohnWileySons,LtdRegisteredofficeJohnWileySonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,POSQ,UnitedKingdomFordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwwwwileycomTherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,DesignsandPatentsActAllrightsreservedNopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,DesignsandPatentsAct,withoutthepriorpermissionofthepublisherWileyalsopublishesitsbooksinavarietyofelectronicformatsSomecontentthatappearsinprintmaynotbeavailableinelectronicbooksDesignationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarksAllbrandnamesandproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespectiveownersThepublisherisnotassociatedwithanyproductorvendormentionedinthisbookThispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmattercoveredItissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesIfprofessionaladviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesoughtLibraryofCongressCataloguinginPublicationDataFan,JinghongMultiscaleanalysisofdeformationandfailureofmaterialsJinghongFanpcmIncludesbibliographicalreferencesandindexISBN(cloth)Deformations(Mechanics)Materials–Analysis–DataprocessingMultivariateanalysisITitleTAF’–dcAcataloguerecordforthisbookisavailablefromtheBritishLibraryPrintISBN:ePDFISBN:oBookISBN:Setinpt,TimesRomanbyThomsonDigital,Noida(India)Tomywife,ZhengYingDaughterYingFanandSonQiangFanforinspirationandlovingsupportContentsAbouttheAuthorxxiSeriesPrefacexxiiiPrefacexxvAbbreviationsxxviiIntroductionMaterialPropertiesBasedonHierarchyofMaterialStructurePropertystructureRelationshipatFundamentalScalePropertystructureRelationshipatDifferentScalesUpgradingProductsBasedonMaterialStructurepropertyRelationshipsExplorationofIndepthMechanismsforDeformationandFailurebyMultiscaleModelingandSimulationOverviewofMultiscaleAnalysisObjectives,ContentsandSignificanceofMultiscaleAnalysisClassificationBasedonMultiscaleModelingSchemesClassificationBasedontheLinkageFeatureattheInterfaceBetweenDifferentScalesFrameworkofMultiscaleAnalysisCoveringaLargeRangeofSpatialScalesTwoClassesofSpatialMultiscaleAnalysisLinksBetweentheTwoClassesofMultiscaleAnalysisDifferentCharacteristicsofTwoClassesofMultiscaleAnalysisMinimumSizeofContinuumExamplesinFormulatingMultiscaleModelsfromPracticeCyclicCreep(Ratcheting)AnalysisofPearliticSteelAcrossMicromesomacroscopicScalesMultiscaleAnalysisforBrittleductileTransitionofMaterialFailureConcludingRemarksReferencesBasicsofAtomisticSimulationTheRoleofAtomisticSimulationCharacteristics,HistoryandTrendsApplicationAreasofAtomisticSimulationAnOutlineofAtomisticSimulationProcessAnExpressionofAtomisticSystemInteratomicForceandPotentialFunctionTheRelationBetweenInteratomicForceandPotentialFunctionPhysicalBackgroundandClassificationsofPotentialFunctionsPairPotentialLennardJones(LJ)PotentialThePairPotentialMorsePotentialUnitsforAtomisticAnalysisandAtomicUnits(au)NumericalAlgorithmsforIntegrationandErrorEstimationMotionEquationofParticlesVerletNumericalAlgorithmVelocityVerlet(VV)AlgorithmOtherAlgorithmsGeometricModelDevelopmentofAtomisticSystemBoundaryConditionsPeriodicBoundaryConditions(PBC)NonPBCandMixedBoundaryConditionsStatisticalEnsemblesNveEnsembleNvtEnsembleNptEnsembleEnergyMinimizationforPreprocessingandStatisticalMechanicsDataAnalysesEnergyMinimizationDataAnalysisBasedonStatisticalMechanicsStatisticalSimulationUsingMonteCarloMethodsIntroductionofStatisticalMethodMetropolisHastingsAlgorithmforStaticsProblemDynamicalMonteCarloSimulationsAdsorptiondesorptionEquilibriumConcludingRemarksReferencesApplicationsofAtomisticSimulationinCeramicsandMetalsPartApplicationsinCeramicsandMaterialswithIonicandCovalentBondsCovalentandIonicPotentialsandAtomisticSimulationforCeramicsApplicationsofHighperformanceCeramicsCeramicAtomicBondsinTermsofElectronegativityBornSolidModelforIonicbondingMaterialsBornModelBornMayerandBuckinghamPotentialsviiiContentsShellModelDeterminationofParametersofShortdistancePotentialforOxidesBasicAssumptionsGeneralMethodsinDeterminingPotentialParametersThreeBasicMethodsforPotentialParameterDeterminationbyExperimentsApplicationsinCeramics:DefectStructureinScandiumDopedCeriaUsingStaticLatticeCalculationApplicationsinCeramics:CombinedStudyofAtomisticSimulationwithXRDforNonstoichiometryMechanismsinYAlO(YAG)GarnetsBackgroundStructureandDefectMechanismsofYAGGarnetsSimulationMethodandResultsApplicationsinCeramics:ConductivityoftheYSZOxideFuelElectrolyteandDomainSwitchingofFerroelectricCeramicsUsingMDMDSimulationoftheMotionofOxygenIonsinSOFCTersoffandBrennerPotentialsforCovalentMaterialsIntroductionoftheAbellTersoffBonderorderApproachTersoffandBrennerPotentialTheAtomisticStressandAtomisticbasedStressMeasureTheVirialStressMeasureTheComputationFormfortheVirialStressTheAtomisticbasedStressMeasureforContinuumPartApplicationsinMetallicMaterialsandAlloysMetallicPotentialsandAtomisticSimulationforMetalsEmbeddedAtomMethodsEAMandMEAMBasicEAMFormulationEAMPhysicalBackgroundEAMApplicationforHydrogenEmbrittlementModifiedEmbeddedAtomMethod(MEAM)SummaryandDiscussionsConstructingBinaryandHighOrderPotentialsfromMonoatomicPotentialsDeterminationofParametersinLJPairFunctionforUnlikeAtomsbyLorentzBertheletMixingRuleDeterminationofParametersinMorseandExponentialPotentialsforUnlikeAtomsDeterminationofParametersinEAMPotentialsforAlloysDeterminationofParametersinMEAMPotentialsforAlloysApplicationExamplesofMetals:MDSimulationRevealsYieldMechanismofMetallicNanowiresCollectingDataofAtomisticPotentialsfromtheInternetBasedonaSpecificTechnicalRequirementBackgroundAboutGalvanicCorrosionofMagnesiumandNanoCeramicsCoatingonSteelPhysicalandChemicalVaporDepositiontoProduceCeramicsThinCoatingLayersonSteelSubstrateContentsixTechnicalRequirementforPotentialsandSearchingResultsUsingObtainedDataforPotentialDevelopmentandAtomisticSimulationAppendixAPotentialTablesforOxidesandThinFilmCoatingLayersReferencesQuantumMechanicsandItsEnergyLinkagewithAtomisticAnalysisDeterminationofUraniumDioxideAtomisticPotentialandtheSignificanceofQMSomeBasicConceptsofQMPostulatesofQMTheSteadyStateSchr€odingerEquationofaSingleParticleExampleSolution:SquarePotentialWellwithInfiniteDepthObservationsandDiscussionsSchr€odingerEquationofMultibodySystemsandCharacteristicsofitsEigenvaluesandGroundStateEnergyGeneralExpressionoftheSchr€odingerEquationandExpectationValueofMultibodySystemsExample:Schr€odingerEquationforHydrogenAtomSystemsVariationPrincipletoDetermineApproximateGroundStateEnergyThreeBasicSolutionMethodsforMultibodyProblemsinQMFirstprincipleorabinitioMethodsAnApproximateMethodTightBindingMethodHartreeFock(HF)MethodsHartreeMethodforaMultibodyProblemHartreeFock(HF)MethodfortheMultibodyProblemElectronicDensityFunctionalTheory(DFT)BriefIntroductiononDevelopingInteratomicPotentialsbyDFTCalculationsEnergyLinkageBetweenQMandAtomisticSimulationMoreInformationaboutBasisSetandPlanewavePseudopotentialMethodforDeterminingAtomisticPotentialUsingSplineFunctionstoExpressPotentialEnergyFunctionsASystematicMethodtoDeterminePotentialFunctionsbyFirstprincipleCalculationsandExperimentalDataConcludingRemarksAppendixASolutiontoIsolatedHydrogenAtomReferencesConcurrentMultiscaleAnalysisbyGeneralizedParticleDynamicsMethodsIntroductionExistingNeedsforConcurrentMultiscaleModelingExpandingModelSizebyConcurrentMultiscaleMethodsApplicationstoNanotechnologyandBiotechnologyPlanforStudyofConcurrentMultiscaleMethodsxContentsTheGeometricModeloftheGPMethodDevelopingNaturalBoundariesBetweenDomainsofDifferentScalesTwoImaginaryDomainsNexttotheScaleBoundaryNeighborlinkCells(NLC)ofImaginaryParticlesMechanismsforSeamlessTransitionLinkageofPositionVectorsatDifferentScalesbySpatialandTemporalAveragingDiscussionsVerificationofSeamlessTransitionviaDModelAnInverseMappingMethodforDynamicsAnalysisofGeneralizedParticlesApplicationsofGPMethodValidationbyComparisonofDislocationInitiationandEvolutionPredictedbyMDandGPValidationbyComparisonofSlipPatternsPredictedbyMDandGPSummaryandDiscussionsStatesofArtofConcurrentMultiscaleAnalysisMAADConcurrentMultiscaleMethodIncompatibilityProblemsatScaleBoundaryIllustratedwiththeMAADMethodQuasicontinuum(QC)MethodCouplingAtomisticAnalysiswithDiscreteDislocation(CADD)MethodExistingEffortstoEliminateArtificialPhenomenaattheBoundaryEmbeddedStatisticalCouplingMethod(ESCM)withCommentsonDirectCoupling(DC)MethodsConclusionConcludingRemarksReferencesQuasicontinuumConcurrentandSemianalyticalHierarchicalMultiscaleMethodsAcrossAtomsContinuumIntroductionPartBasicEnergyPrincipleandNumericalSolutionTechniquesinSolidMechanicsPrincipleofMinimumPotentialEnergyofSolidsandStructuresStrainEnergyDensityC�WorkPotentialEssentialPointsofFiniteElementMethodsDiscretizationofContinuumDomainBCintoFiniteElementsUsingGaussianQuadraturetoCalculateElementEnergyWorkPotentialExpressedbyNodeDisplacementMatrixTotalPotentialEnergyPExpressedbyNodeDisplacementMatrixDevelopingSimultaneousAlgebraicEquationsforNodalDisplacementMatrixContentsxiPartQuasicontinuum(QC)ConcurrentMethodofMultiscaleAnalysisTheIdeaandFeaturesoftheQCMethodFormulationofRepresentativeAtomsandTotalPotentialEnergyintheQCMethodUsingInterpolationFunctionstoReduceDegreesofFreedomModelDivisionUsingtheCauchyBornRuletoCalculateEnergyDensityFunctionWfromInteratomicPotentialEnergyTheSolutionSchemeoftheQCMethodSubroutinetoDetermineEnergyDensityWforEachElementTreatmentoftheInterfaceGhostForceFullyNonlocalizedQCMethodEnergybasedNonlocalQCModel(CQC(m)E)DeadGhostForceCorrectioninEnergybasedNonlocalQCApplicationsoftheQCMethodNanoindentationCracktipDeformationDeformationandFractureofGrainBoundariesDislocationInteractionsPolarizationsSwitchinginFerroelectricsShortDiscussionabouttheQCMethodPartAnalyticalandSemianalyticalMultiscaleMethodsAcrossAtomicContinuumScalesMoreDiscussionsaboutDeformationGradientandtheCauchyBornRuleMathematicalDefinitionofDeformationGradientF(�X)DeterminationofLatticeVectorsandAtomPositionsbytheCauchyBornRulethroughDeformationGradientFPhysicalExplanationsofComponentsofDeformationGradientExpressionsofFandeComponentsinTermsofDisplacementVectorTheRelationshipBetweenDeformationGradient,StrainandStressTensorsAnalyticalSemianalyticalMethodsAcrossAtomContinuumScalesBasedontheCauchyBornRuleApplicationoftheCauchyBornRuleinaCentrosymmetricStructureDeterminationofInteratomicLengthrijandAngleyijkoftheCrystalafterDeformationbytheCauchyBornRuleAShortDiscussiononthePrecisionoftheCauchyBornRuleAtomisticbasedContinuumModelofHydrogenStoragewithCarbonNanotubesIntroductionofTechnicalBackgroundandThreeTypesofNanotubesInteratomicPotentialsUsedforAtomContinuumTransitionTheAtomisticbasedContinuumTheoryofHydrogenStoragexiiContentsAtomisticbasedContinuumModelingtoDeterminetheHydrogenDensityandPressurepContinuumModelofInteractionsBetweentheCNTandHydrogenMoleculesandConcentrationofHydrogenAnalyticalSolutionfortheConcentrationofHydrogenMoleculesTheDoubleWallEffectsonHydrogenStorageAtomisticbasedModelforMechanical,ElectricalandThermalPropertiesofNanotubesHighlightsoftheMethodsMechanicalPropertiesElectricalPropertyChangeinDeformableConductorsThermalPropertiesOtherWorkinAtomisticbasedContinuumModelAProofofDInverseMappingRuleoftheGPMethodConcludingRemarksReferencesFurtherIntroductiontoConcurrentMultiscaleMethodsGeneralFeatureinGeometryofConcurrentMultiscaleModelingInterfaceDesignoftheDCMultiscaleModelsConnectionandCompatibilityBetweenAtomContinuumattheInterfacePhysicalFeaturesofConcurrentMultiscaleModelsEnergybasedandForcebasedFormulationConstitutiveLawsintheFormulationMAADMethodforAnalysisAcrossabinitio,AtomicandMacroscopicScalesPartitioningandCouplingofModelRegionSystemEnergyandHamiltonianinDifferentRegionsHandshakeRegionDesignShortDiscussionontheMAADMethodForcebasedFormulationofConcurrentMultiscaleModelingCoupledAtomDiscreteDislocationDynamics(CADD)MultiscaleMethodRealizationofForcebasedFormulationforCADDFEAtBasicModelforCADDSolutionScheme:ASuperpositionofThreeTypesofBoundaryValueProblemsDModelforaMultiscaleDynamicAnalysisTheInternalForceandEquivalentMassofaDynamicSystemDerivationoftheFEMDCoupledMotionEquationNumericalExampleoftheCouplingBetweenMDandFEResultsandDiscussionBridgingDomainsMethodDBenchmarkTestsofInterfaceCompatibilityforDCMethodsSystematicPerformanceBenchmarkofMostDCAtomisticContinuumCouplingMethodsContentsxiiiTheBenchmarkComputationTestSummaryandConclusionoftheBenchmarkTestTheEmbeddedStatisticalCouplingMethod(ESCM)WhyDoesESCMUseStatisticalAveragingtoReplaceDC’sDirectLinkageTheESCMModelMDFEInterfaceSurfaceMDRegionValidationReferencesHierarchicalMultiscaleMethodsforPlasticityAMethodologyofHierarchicalMultiscaleAnalysisAcrossMicromesomacroscopicScalesandInformationTransformationBetweenTheseScalesSchematicViewofHierarchicalMultiscaleAnalysisUsingTwofaceFeatureofMesocelltoLinkBothMicroscopicandMacroscopicScalesQuantitativeMesomacroBridgingBasedonSelfconsistentSchemesBasicAssumptionIntroductiontoSelfconsistentSchemes(SCS)WeakeningConstraintEffectofAggregateonInclusionwithIncreaseofPlasticDeformationQuantitativeLinkageofVariablesBetweenMesoscopicandMacroscopicScalesBasicsofContinuumPlasticityTheorySeveralBasicElementsofContinuumPlasticityTheoryDescriptionofContinuumPlasticityTheoryWithinDeviatoricStressSpaceInternalVariableTheory,BackStressandElastoplasticConstitutiveEquationsInternalVariableTheoryExpressedbyaMechanicalModelCalculationofBackStressRijinTermsofPlasticStrainExpressingElastoplasticConstitutiveEquationsforEachConstituentPhaseQuantitativeMicromesoBridgingbyDevelopingMesocellConstitutiveEquationsBasedonMicroscopicAnalysisDevelopingMesocell(Inclusion)ConstitutiveEquationsBridgingMicroandMacroscopicVariablesviatheMesocellConstitutiveEquationSolutionTechniqueDeterminingSizeEffectonYieldS

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