Advanced Computational Materials Modeling: From Classical to Multi-Scale Techniques

446 Pages·6.295 MB·English

Editedby
MiguelVazJu´nior,
EduardoA.deSouzaNeto,and
PabloA.Mun˜oz-Rojas
AdvancedComputationalMaterials
Modeling
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Edited by Miguel Vaz Ju´nior, Eduardo A. de Souza Neto, and
Pablo A. Mun˜oz-Rojas
Advanced Computational Materials Modeling
From Classical to Multi-Scale Techniques
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ISBN:978-3-527-32479-8
V
Contents
Preface XIII
ListofContributors XV
1 MaterialsModeling– ChallengesandPerspectives 1
MiguelVazJr.,EduardoA.deSouzaNeto,andPabloAndre´sMun˜oz-Rojas
1.1 Introduction 1
1.2 ModelingChallengesandPerspectives 3
1.2.1 MechanicalDegradationandFailureofDuctileMaterials 3
1.2.1.1 Remarks 7
1.2.2 ModelingofCellularStructures 8
1.2.2.1 Remarks 14
1.2.3 MultiscaleConstitutiveModeling 15
1.3 ConcludingRemarks 18
Acknowledgments 19
References 19
2 LocalandNonlocalModelingofDuctileDamage 23
Jose´ManueldeAlmeidaCe´sardeSa´,FranciscoManuelAndradePires,
andFilipeXavierCostaAndrade
2.1 Introduction 23
2.2 ContinuumDamageMechanics 25
2.2.1 BasicConceptsofCDM 25
2.2.2 DuctilePlasticDamage 26
2.3 Lemaitre’sDuctileDamageModel 27
2.3.1 OriginalModel 27
2.3.1.1 TheElasticStatePotential 28
2.3.1.2 ThePlasticStatePotential 29
2.3.1.3 TheDissipationPotential 29
2.3.1.4 EvolutionofInternalVariables 30
2.3.2 PrincipleofMaximumInelasticDissipation 31
2.3.3 AssumptionsBehindLemaitre’sModel 32
2.4 ModifiedLocalDamageModels 33
2.4.1 Lemaitre’sSimplifiedDamageModel 33
AdvancedComputationalMaterialsModeling:FromClassicaltoMulti-ScaleTechniques.
EditedbyMiguelVazJu´nior,EduardoA.deSouzaNeto,andPabloA.Munoz-Rojas
Copyright2011WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-32479-8
VI Contents
2.4.1.1 ConstitutiveModel 33
2.4.1.2 NumericalImplementation 34
2.4.2 DamageModelwithCrackClosureEffect 37
2.4.2.1 ConstitutiveModel 37
2.4.2.2 NumericalImplementation 40
2.5 NonlocalFormulations 42
2.5.1 AspectsofNonlocalAveraging 44
2.5.1.1 TheAveragingOperator 44
2.5.1.2 WeightFunctions 45
2.5.2 ClassicalNonlocalModelsofIntegralType 45
2.5.2.1 NonlocalFormulationsforLemaitre’sSimplifiedModel 46
2.5.3 NumericalImplementationofNonlocalIntegralModels 47
2.5.3.1 NumericalEvaluationoftheAveragingIntegral 48
2.5.3.2 GlobalVersionoftheElasticPredictor/ReturnMappingAlgorithm 49
2.6 NumericalAnalysis 57
2.6.1 AxisymmetricAnalysisofaNotchedSpecimen 57
2.6.2 FlatGroovedPlateinPlaneStrain 62
2.6.3 UpsettingofaTaperedSpecimen 63
2.6.3.1 DamagePredictionUsingtheLemaitre’sSimplifiedModel 65
2.6.3.2 DamagePredictionUsingtheLemaitre’sModelwithCrackClosure
Effect 67
2.7 ConcludingRemarks 68
Acknowledgments 69
References 69
3 RecentAdvancesinthePredictionoftheThermalPropertiesofMetallic
HollowSphereStructures 73
ThomasFiedler,IrinaV.Belova,GraemeE.Murch,andAndreasO¨chsner
3.1 Introduction 73
3.2 Methodology 74
3.2.1 LatticeMonteCarloMethod 75
3.2.2 FiniteElementMethod 77
3.2.2.1 BasicsofHeatTransfer 77
3.2.2.2 WeightedResidualMethod 77
3.2.2.3 DiscretizationandPrincipalFiniteElementEquation 78
3.2.3 NumericalCalculationModels 89
3.3 FiniteElementAnalysisonRegularStructures 91
3.4 FiniteElementAnalysisonCubic-SymmetricModels 94
3.5 LMCAnalysisofModelsofCrossSections 98
3.5.1 Modeling 98
3.5.2 Results 101
3.6 ComputedTomographyReconstructions 103
3.6.1 ComputedTomography 104
3.6.2 NumericalAnalysis 104
3.6.2.1 Microstructure 105
Contents VII
3.6.2.2 Mesostructure 106
3.6.3 Results 106
3.7 Conclusions 108
References 109
4 ComputationalHomogenizationforLocalizationandDamage 111
ThierryJ.Massart,VarvaraKouznetsova,RonH.J.Peerlings,andMarc
G.D.Geers
4.1 Introduction 111
4.1.1 MechanicsAcrosstheScales 111
4.1.2 SomeHistoricalNotesonHomogenization 112
4.1.3 SeparationofScales 113
4.1.4 ComputationalHomogenizationandItsApplicationtoDamageand
Fracture 114
4.2 Continuous–ContinuousScaleTransitions 115
4.2.1 First-OrderComputationalHomogenization 115
4.2.2 Second-OrderComputationalHomogenization 119
4.2.3 ApplicationoftheContinuous–ContinuousHomogenizationSchemes
toDuctileDamage 121
4.3 Continuous–DiscontinuousScaleTransitions 125
4.3.1 ScaleTransitionsandRVEforInitiallyPeriodicMaterials 126
4.3.1.1 First-OrderScaleTransitions 126
4.3.1.2 ChoiceoftheMesoscopicRepresentativeVolumeElement 127
4.3.1.3 BoundaryConditionsfortheUnitCell 128
4.3.2 LocalizationofDamageattheFineandCoarseScales 129
4.3.2.1 Fine-ScaleLocalization – ImplicitGradientDamage 129
4.3.2.2 DetectionofCoarse-ScaleLocalizationasaBifurcationintoan
InhomogeneousDeformationPattern 130
4.3.2.3 IllustrationoftheLocalizationAnalysis 132
4.3.2.4 IdentificationandSelectionoftheLocalizationOrientation 135
4.3.3 LocalizationBandEnhancedMultiscaleSolutionScheme 135
4.3.3.1 IntroductionoftheLocalizationBand 136
4.3.3.2 CoupledMultiscaleSchemeforLocalization 137
4.3.4 ScaleTransitionProcedureforLocalizedBehavior 139
4.3.4.1 MultiscaleSolutionProcedure 139
4.3.4.2 CausesofSnapbackintheAveragedMaterialResponse 139
4.3.4.3 StrainJumpControlforEmbeddedBandSnapback 140
4.3.4.4 DissipationControlforUnit-CellSnapback 141
4.3.5 SolutionStrategyandComputationalAspects 142
4.3.5.1 GoverningEquationsfortheMacroscopicandMesoscopicSolution
Procedures 142
4.3.5.2 ExtractionofConsistentTangentStiffnessforUnit-CellSnapback
Control 144
4.3.5.3 DiscretizationandLinearizationoftheMacroscopicSolution
Procedure 144
VIII Contents
4.3.5.4 IntroductionofLocalizationBandsuponMaterialBifurcation 146
4.3.6 ApplicationsandDiscussion 147
4.3.6.1 SelectionofLocalizedSolutions 147
4.3.6.2 MesostructuralSnapbackinaTension–CompressionTest 149
4.3.6.3 SizeEffectinaShear–CompressionTest 151
4.3.6.4 MasonryShearWallTest 152
4.4 ClosingRemarks 159
References 160
5 AMixedOptimizationApproachforParameterIdentificationAppliedto
theGursonDamageModel 165
PabloAndre´sMun˜oz-Rojas,LuizAntonioB.daCunda,EduardoL.
Cardoso,MiguelVazJr.,andGuillermoJuanCreus
5.1 Introduction 165
5.2 GursonDamageModel 166
5.2.1 InfluenceoftheParameterValuesonBehavioroftheDamage
Model 171
5.2.2 RecentDevelopmentsandNewTrendsintheGursonModel 175
5.3 ParameterIdentification 177
5.4 OptimizationMethods – GeneticAlgorithmsandMathematical
Programming 179
5.4.1 GeneticAlgorithms 180
5.4.1.1 Formulation 181
5.4.1.2 Implementation 184
5.4.2 Gradient-BasedMethods 184
5.4.2.1 GeneralProcedure 184
5.4.2.2 SequentialLinearProgramming(SLP) 185
5.4.2.3 GloballyConvergentMethodofMovingAsymptotes(GCMMA) 185
5.5 SensitivityAnalysis 187
5.5.1 ModifiedFiniteDifferencesandtheSemianalyticalMethod 188
5.6 AMixedOptimizationApproach 192
5.7 ExamplesofApplication 192
◦
5.7.1 LowCarbonSteelat25 C 192
◦
5.7.2 AluminumAlloyat400 C 197
5.8 ConcludingRemarks 200
Acknowledgments 200
References 201
6 SemisolidMetallicAlloysConstitutiveModelingfortheSimulationof
ThixoformingProcesses 205
RoxaneKoeuneandJean-PhilippePonthot
6.1 Introduction 205
6.2 SemisolidMetallicAlloysFormingProcesses 207
6.2.1 ThixotropicSemisolidMetallicAlloys 208
6.2.2 DifferentTypesofSemisolidProcessing 209
Contents IX
6.2.2.1 ProductionofSpheroidalMicrostructure 210
6.2.2.2 Reheating 212
6.2.2.3 Forming 213
6.2.3 AdvantagesandDisadvantagesofSemisolidProcessing 215
6.3 RheologicalAspects 216
6.3.1 MicroscopicPointofView 216
6.3.1.1 OriginsofThixotropy 216
6.3.1.2 TransientBehavior 217
6.3.1.3 EffectiveLiquidFraction 222
6.3.2 MacroscopicPointofView 222
6.3.2.1 TemperatureEffects 222
6.3.2.2 YieldStress 222
6.3.2.3 Macrosegregation 223
6.4 NumericalBackgroundinLargeDeformations 223
6.4.1 KinematicsinLargeDeformations 223
6.4.1.1 LagrangianVersusEulerianCoordinateSystems 223
6.4.1.2 DeformationGradientandStrainRateTensors 225
6.4.2 FiniteDeformationConstitutiveTheory 225
6.4.2.1 PrincipleofObjectivity 225
6.4.2.2 DifferentClassesofMaterials 226
6.4.2.3 ACorotationalFormulation 228
6.4.2.4 LinearElasticSolidMaterialModel 229
6.4.2.5 LinearNewtonianLiquidMaterialModel 230
6.4.2.6 HypoelasticSolidMaterialModels 231
6.4.2.7 LiquidMaterialModels 236
6.4.2.8 ComparisonofSolidandLiquidApproaches 236
6.5 State-of-the-ArtinFE-ModelingofThixotropy 237
6.5.1 One-PhaseModels 237
6.5.1.1 ApparentViscosityEvolution 238
6.5.1.2 YieldStressEvolution 243
6.5.2 Two-PhaseModels 244
6.5.2.1 TwoCoupledFields 244
6.5.2.2 CouplingSources 245
6.6 ADetailedOne-PhaseModel 246
6.6.1 CohesionDegree 247
6.6.2 LiquidFraction 248
6.6.3 ViscosityLaw 248
6.6.4 YieldStressandIsotropicHardening 250
6.7 NumericalApplications 250
6.7.1 TestDescription 250
6.7.2 ResultsAnalysis 251
6.7.2.1 FirstValidationoftheModelunderIsothermalConditions 251
6.7.2.2 ThermomechanicalAnalysis 252
6.7.2.3 ResidualStressesAnalysis 253
6.7.2.4 InternalVariablesAnalysis 253
X Contents
6.8 Conclusion 254
References 255
7 ModelingofPowderFormingProcesses;Applicationofa
Three-invariantCapPlasticityandanEnrichedArbitrary
Lagrangian–EulerianFEMethod 257
AmirR.Khoei
7.1 Introduction 257
7.2 Three-InvariantCapPlasticity 260
7.2.1 IsotropicandKinematicMaterialFunctions 262
7.2.2 ComputationofPowderPropertyMatrix 264
7.2.3 ModelAssessmentandParameterDetermination 265
7.2.3.1 ModelAssessment 265
7.2.3.2 ParameterDetermination 267
7.3 ArbitraryLagrangian–EulerianFormulation 269
7.3.1 ALEGoverningEquations 270
7.3.2 WeakFormofALEEquations 272
7.3.3 ALEFiniteElementDiscretization 273
7.3.4 UncoupledALESolution 274
7.3.4.1 Material(Lagrangian)Phase 275
7.3.4.2 SmoothingPhase 276
7.3.4.3 Convection(Eulerian)Phase 278
7.3.5 NumericalModelingofanAutomotiveComponent 279
7.4 EnrichedALEFiniteElementMethod 282
7.4.1 TheExtended-FEMFormulation 283
7.4.2 AnEnrichedALEFiniteElementMethod 286
7.4.2.1 LevelSetUpdate 287
7.4.2.2 StressUpdateandNumericalIntegration 288
7.4.3 NumericalModelingoftheCoiningTest 291
7.5 Conclusion 295
Acknowledgments 295
References 296
8 FunctionallyGradedPiezoelectricMaterialSystems – AMultiphysics
Perspective 301
WilfredoMontealegreRubio,SandroLuisVatanabe,Gla´ucioHermogenes
Paulino,andEm´ılioCarlosNelliSilva
8.1 Introduction 301
8.2 Piezoelectricity 302
8.3 FunctionallyGradedPiezoelectricMaterials 304
8.3.1 FunctionallyGradedMaterials(FGMs) 304
8.3.2 FGMConceptAppliedtoPiezoelectricMaterials 306
8.4 FiniteElementMethodforPiezoelectricStructures 309
8.4.1 TheVariationalFormulationforPiezoelectricProblems 309
8.4.2 TheFiniteElementFormulationforPiezoelectricProblems 310