Computational Methods for Debonding in Composites

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xii Contents 8.2.4 Modelling Effects of Mechanical (or “Internal”) FrictiononProgressiveFailureDevelopment ..........164 8.2.5 Modelling Progressive Failure in Matrix Dominated Modes...........................................166 8.2.6 Validationofthe3DPlasticityModel.................167 8.3 Modelling Strain Rate Effects in Compression . . . ..............168 8.3.1 Premise and Outline Modelling Approach .............168 8.3.2 ShearStrainRateDependentBehaviour...............168 8.3.3 Modelling Strain Rate Effects in Matrix Dominated ModesofDeformation .............................169 8.3.4 Validation of the 3D Strain-Rate Dependent Plasticity Model...........................................169 8.4 Strain-Rate Dependent Energy-Based Damage Mechanics Approach................................................170 8.5 ValidationoftheImpactDamageModel ......................174 8.6 Conclusions..............................................175 References.....................................................177 9 Progressive Damage Modeling of Composite Materials Under Both Tensile and Compressive Loading Regimes ........... 179 N. Zobeiry, A. Forghani, C. McGregor, R. Vaziri, and A. Poursartip 9.1 Introduction . . ............................................179 9.2 DescriptionoftheCODAMModel...........................183 9.3 ModelCalibration.........................................185 9.4 ModelValidation .........................................188 9.4.1 SimulationofOCTTest ............................188 9.4.2 SimulationofOpenHolePlatesUnderCompression....189 9.5 Non-localApproach.......................................190 9.5.1 LimitationsofLocalDamageModels.................190 9.5.2 Non-localRegularization ...........................191 9.6 Conclusions..............................................193 References.....................................................194 10 Elastoplastic Modeling of Multi-phase Metal Matrix Composite with Void Growth Using the Transformation Field Analysis and Governing Parameter Method ............................. 197 Ernest T.Y. Ng and Afzal Suleman 10.1 Introduction . . ............................................197 10.2 Micromechanics ..........................................199 10.2.1 Setting the Stage ..................................199 10.2.2 GoverningTFAEquations ..........................200 10.3 GPMAlgorithm ..........................................202 10.4 Gurson-TvergaardModelinGPM ...........................203 10.4.1 Gurson-TvergaardYieldCriterion....................203 10.4.2 Newton’sMethod .................................205 10.4.3 Ranges of ∆e P m and ∆ē P ............................206
Contents xiii 10.5 VerificationsandExamples .................................210 10.5.1 TestCases........................................210 10.5.2 DiscussionontheEvaluationProcess.................215 10.5.3 4-phaseCompositeMaterial.........................216 10.6 ClosingRemarks..........................................219 Appendix–Thefourpartialderivatives.............................219 References.....................................................220 11 Prediction of Mechanical Properties of Composite Materials by Asymptotic Expansion Homogenisation ...................... 223 J.A. Oliveira, J. Pinho-da-Cruz, and F. Teixeira-Dias 11.1 Introduction . . ............................................224 11.2 AsymptoticExpansionHomogenisation ......................224 11.2.1 AEHinLinearElasticity ...........................224 11.2.2 Localisation Methodology . . ........................228 11.3 FiniteElementMethodinAEH..............................229 11.3.1 Corrector χ ......................................229 11.3.2 Periodicity Boundary Conditions . ...................229 11.3.3 Homogenised Elasticity Matrix D h ...................230 11.4 NumericalProcedures .....................................230 11.4.1 TheMainProgram ................................230 11.4.2 RepresentativeUnit-CellGeneration..................231 11.4.3 AutomaticAssociationofDegreesofFreedom.........231 11.5 NumericalApplications....................................233 11.6 FinalRemarks............................................240 References.....................................................241 12 On Buckling Optimization of a Wind Turbine Blade .............. 243 Erik Lund and Leon S. Johansen 12.1 Introduction . . ............................................243 12.2 DiscreteMaterialOptimization(DMO)Approach..............245 12.2.1 Parametrization for Single Layered Laminate Structures . 246 12.2.2 Parametrization for Multi Layered Laminate Structures . . 247 12.2.3 PatchDesignVariables.............................247 12.2.4 DMOConvergence................................247 12.3 AnalysisandDesignSensitivityAnalysis .....................248 12.4 TheOptimizationProblem..................................249 12.5 BucklingOptimizationofWindTurbineBladeTestSection......250 12.6 Conclusion...............................................258 References.....................................................258 13 Computation of Effective Stiffness Properties for Textile-Reinforced Composites Using X-FEM .................................... 261 M. Kästner, G. Haasemann, J. Brummund, and V. Ulbricht 13.1 Homogenization ..........................................261 13.1.1 Boundary Conditions and Deformation Modes .........264
Page 2 and 3: Mechanical Response of Composites
Page 4 and 5: Pedro P. Camanho • C.G. Dávila S
Page 6 and 7: Preface The methodology for designi
Page 8 and 9: Acknowledgements The Editors of thi
Page 10 and 11: x Contents 3 Practical Challenges i
Page 14 and 15: xiv Contents 13.1.2 EffectiveProper
Page 16 and 17: xvi List of Contributors Clara Schu
Page 18 and 19: Chapter 1 Computational Methods for
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48 R. Rolfes et al. A dev is the de
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50 R. Rolfes et al. uniaxial compre
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52 R. Rolfes et al. Stress in MPa -
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54 R. Rolfes et al. 2.4.2 Results o
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56 R. Rolfes et al. 12. Hughes TJR
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58 B.N. Cox et al. inform models; a
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60 B.N. Cox et al. 3.2 The Structur
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62 B.N. Cox et al. be successfully
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64 B.N. Cox et al. high fluxes of c
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68 B.N. Cox et al. For example, a c
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72 B.N. Cox et al. mixed-mode crack
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Chapter 4 Analytical and Numerical
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4 Analytical and Numerical Investig
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Chapter 6 Study of Delamination in
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6 Study of Delamination with in Com
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7 Interaction Between Intraply and
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Chapter 8 A Numerical Material Mode
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8 A Numerical Material Model for Pr
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182 N. Zobeiry et al. for construct
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184 N. Zobeiry et al. In compressio
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186 N. Zobeiry et al. c = 38.7 mm h
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188 N. Zobeiry et al. displacement
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190 N. Zobeiry et al. No Notched St
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192 N. Zobeiry et al. where g f is
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194 N. Zobeiry et al. References 1.
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Chapter 10 Elastoplastic Modeling o
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10 Elastoplastic Modeling of Multi-
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234 J.A. Oliveira et al. Fig. 11.7
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14 Development of DST for the Model
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306 H. Miled et al. Eqs. 15.28 and
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310 H. Miled et al. Fig. 15.13 Comp
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312 H. Miled et al. 9. Carreau P, D
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