Advanced Computational Materials Modeling

Miguel Vaz Jr. heads the research group "Development and Application of Numerical Methods to Continuum Mechanics" at the State University of Santa Catarina, Brazil. He received his Ph.D. in Civil Engineering in 1998 from the Swansea University, UK. He has worked in multi-physics and coupled problems, especially computational plasticity, thermo-mechanical coupling and polymer melt flow.Eduardo A. de Souza Neto is a Reader at the School of Engineering, Swansea University, UK. He received his Ph.D. in 1994 from Swansea University for his work in computational plasticity. He has dedicated his research activities to the development of constitutive models and numerical algorithms aimed at large strain inelasticity. He authored key papers on finite element technology, finite strain plasticity and damage mechanics and has been more recently publishing articles on multi-scale methods in non-linear solid mechanics. He is also the author of a textbook on computational methods for plasticity.Pablo Andrés Muñoz-Rojas leads the "Computational Mechanics Laboratory" at the State University of Santa Catarina, Brazil. He obtained his Ph.D. degree at the Federal University of Rio Grande do Sul, Brazil, with research on the application of optimization techniques to metal forming problems. He has focused his work on numerical techniques for sensitivity analysis, parameter identification of elastic-plastic properties and viscoelasticity.

• Preface XIIIList of Contributors XV1 Materials Modeling – Challenges and Perspectives 1Miguel Vaz Jr., Eduardo A. de Souza Neto, and Pablo Andre´s Muñoz-Rojas1.1 Introduction 11.2 Modeling Challenges and Perspectives 31.2.1 Mechanical Degradation and Failure of Ductile Materials 31.2.2 Modeling of Cellular Structures 81.2.3 Multiscale Constitutive Modeling 151.3 Concluding Remarks 18Acknowledgments 19References 192 Local and Nonlocal Modeling of Ductile Damage 23José Manuel de Almeida César de Sá, Francisco Manuel Andrade Pires, and Filipe Xavier Costa Andrade2.1 Introduction 232.2 Continuum Damage Mechanics 252.2.1 Basic Concepts of CDM 252.2.2 Ductile Plastic Damage 262.3 Lemaitre’s Ductile Damage Model 272.3.1 Original Model 272.3.2 Principle of Maximum Inelastic Dissipation 312.3.3 Assumptions Behind Lemaitre’s Model 322.4 Modified Local Damage Models 332.4.1 Lemaitre’s Simplified Damage Model 332.4.2 Damage Model with Crack Closure Effect 372.5 Nonlocal Formulations 422.5.1 Aspects of Nonlocal Averaging 442.5.2 Classical Nonlocal Models of Integral Type 452.5.3 Numerical Implementation of Nonlocal Integral Models 472.6 Numerical Analysis 572.6.1 Axisymmetric Analysis of a Notched Specimen 572.6.2 Flat Grooved Plate in Plane Strain 622.6.3 Upsetting of a Tapered Specimen 632.7 Concluding Remarks 68Acknowledgments 69References 693 Recent Advances in the Prediction of the Thermal Properties of Metallic Hollow Sphere Structures 73Thomas Fiedler, Irina V. Belova, Graeme E. Murch, and Andreas Öchsner3.1 Introduction 733.2 Methodology 743.2.1 Lattice Monte Carlo Method 753.2.2 Finite Element Method 773.2.3 Numerical Calculation Models 893.3 Finite Element Analysis on Regular Structures 913.4 Finite Element Analysis on Cubic-Symmetric Models 943.5 LMC Analysis of Models of Cross Sections 983.5.1 Modeling 983.5.2 Results 1013.6 Computed Tomography Reconstructions 1033.6.1 Computed Tomography 1043.6.2 Numerical Analysis 1043.6.3 Results 1063.7 Conclusions 108References 1094 Computational Homogenization for Localization and Damage 111Thierry J. Massart, Varvara Kouznetsova, Ron H. J. Peerlings, and Marc G. D. Geers4.1 Introduction 1114.1.1 Mechanics Across the Scales 1114.1.2 Some Historical Notes on Homogenization 1124.1.3 Separation of Scales 1134.1.4 Computational Homogenization and Its Application to Damage and Fracture 1144.2 Continuous–Continuous Scale Transitions 1154.2.1 First-Order Computational Homogenization 1154.2.2 Second-Order Computational Homogenization 1194.2.3 Application of the Continuous–Continuous Homogenization Schemes to Ductile Damage 1214.3 Continuous–Discontinuous Scale Transitions 1254.3.1 Scale Transitions and RVE for Initially Periodic Materials 1264.3.2 Localization of Damage at the Fine and Coarse Scales 1294.3.3 Localization Band Enhanced Multiscale Solution Scheme 1354.3.4 Scale Transition Procedure for Localized Behavior 1394.3.5 Solution Strategy and Computational Aspects 1424.3.6 Applications and Discussion 1474.4 Closing Remarks 159References 1605 A Mixed Optimization Approach for Parameter Identification Applied to the Gurson Damage Model 165Pablo Andre´s Muñoz-Rojas, Luiz Antonio B. da Cunda, Eduardo L. Cardoso, Miguel Vaz Jr., and Guillermo Juan Creus5.1 Introduction 1655.2 Gurson Damage Model 1665.2.1 Influence of the Parameter Values on Behavior of the Damage Model 1715.2.2 Recent Developments and New Trends in the Gurson Model 1755.3 Parameter Identification 1775.4 Optimization Methods – Genetic Algorithms and Mathematical Programming 1795.4.1 Genetic Algorithms 1805.4.2 Gradient-Based Methods 1845.5 Sensitivity Analysis 1875.5.1 Modified Finite Differences and the Semianalytical Method 1885.6 A Mixed Optimization Approach 1925.7 Examples of Application 1925.7.1 Low Carbon Steel at 25 ◦C 1925.7.2 Aluminum Alloy at 400 ◦C 1975.8 Concluding Remarks 200Acknowledgments 200References 2016 Semisolid Metallic Alloys Constitutive Modeling for the Simulation of Thixoforming Processes 205Roxane Koeune and Jean-Philippe Ponthot6.1 Introduction 2056.2 Semisolid Metallic Alloys Forming Processes 2076.2.1 Thixotropic Semisolid Metallic Alloys 2086.2.2 Different Types of Semisolid Processing 2096.2.3 Advantages and Disadvantages of Semisolid Processing 2156.3 Rheological Aspects 2166.3.1 Microscopic Point of View 2166.3.2 Macroscopic Point of View 2226.4 Numerical Background in Large Deformations 2236.4.1 Kinematics in Large Deformations 2236.4.2 Finite Deformation Constitutive Theory 2256.5 State-of-the-Art in FE-Modeling of Thixotropy 2376.5.1 One-Phase Models 2376.5.2 Two-Phase Models 2446.6 A Detailed One-Phase Model 2466.6.1 Cohesion Degree 2476.6.2 Liquid Fraction 2486.6.3 Viscosity Law 2486.6.4 Yield Stress and Isotropic Hardening 2506.7 Numerical Applications 2506.7.1 Test Description 2506.7.2 Results Analysis 2516.8 Conclusion 254References 2557 Modeling of Powder Forming Processes; Application of a Three-invariant Cap Plasticity and an Enriched Arbitrary Lagrangian–Eulerian FE Method 257Amir R. Khoei7.1 Introduction 2577.2 Three-Invariant Cap Plasticity 2607.2.1 Isotropic and Kinematic Material Functions 2627.2.2 Computation of Powder Property Matrix 2647.2.3 Model Assessment and Parameter Determination 2657.3 Arbitrary Lagrangian–Eulerian Formulation 2697.3.1 ALE Governing Equations 2707.3.2 Weak Form of ALE Equations 2727.3.3 ALE Finite Element Discretization 2737.3.4 Uncoupled ALE Solution 2747.3.5 Numerical Modeling of an Automotive Component 2797.4 Enriched ALE Finite Element Method 2827.4.1 The Extended-FEM Formulation 2837.4.2 An Enriched ALE Finite Element Method 2867.4.3 Numerical Modeling of the Coining Test 2917.5 Conclusion 295Acknowledgments 295References 2968 Functionally Graded Piezoelectric Material Systems – A Multiphysics Perspective 301Wilfredo Montealegre Rubio, Sandro Luis Vatanabe, Gláucio Hermogenes Paulino, and Emílio Carlos Nelli Silva8.1 Introduction 3018.2 Piezoelectricity 3028.3 Functionally Graded Piezoelectric Materials 3048.3.1 Functionally Graded Materials (FGMs) 3048.3.2 FGM Concept Applied to Piezoelectric Materials 3068.4 Finite Element Method for Piezoelectric Structures 3098.4.1 The Variational Formulation for Piezoelectric Problems 3098.4.2 The Finite Element Formulation for Piezoelectric Problems 3108.4.3 Modeling Graded Piezoelectric Structures by Using the FEM 3128.5 Influence of Property Scale in Piezotransducer Performance 3148.5.1 Graded Piezotransducers in Ultrasonic Applications 3148.5.2 Further Consideration of the Influence of Property Scale: Optimal Material Gradation Functions 3198.6 Influence of Microscale 3228.6.1 Performance Characteristics of Piezocomposite Materials 3268.6.2 Homogenization Method 3288.6.3 Examples 3328.7 Conclusion 335Acknowledgments 335References 3369 Variational Foundations of Large Strain Multiscale Solid Constitutive Models: Kinematical Formulation 341Eduardo A. de Souza Neto and Rául A. Feijóo9.1 Introduction 3419.2 Large Strain Multiscale Constitutive Theory: Axiomatic Structure 3439.2.1 Deformation Gradient Averaging and RVE Kinematics 3469.2.2 Actual Constraints: Spaces of RVE Velocities and Virtual Displacements 3489.2.3 Equilibrium of the RVE 3499.2.4 Stress Averaging Relation 3519.2.5 The Hill–Mandel Principle of Macrohomogeneity 3529.3 The Multiscale Model Definition 3539.3.1 The Microscopic Equilibrium Problem 3549.3.2 The Multiscale Model: Well-Posed Equilibrium Problem 3549.4 Specific Classes of Multiscale Models: The Choice of Vμ 3569.4.1 Taylor Model 3569.4.2 Linear RVE Boundary Displacement Model 3599.4.3 Periodic Boundary Displacement Fluctuations Model 3599.4.4 Minimum Kinematical Constraint: Uniform Boundary Traction 3609.5 Models with Stress Averaging in the Deformed RVE Configuration 3619.6 Problem Linearization: The Constitutive Tangent Operator 3629.6.1 Homogenized Constitutive Functional 3639.6.2 The Homogenized Tangent Constitutive Operator 3649.7 Time-Discrete Multiscale Models 3669.7.1 The Incremental Equilibrium Problem 3679.7.2 The Homogenized Incremental Constitutive Function 3679.7.3 Time-Discrete Homogenized Constitutive Tangent 3689.8 The Infinitesimal Strain Theory 3719.9 Concluding Remarks 372Appendix 373Acknowledgments 376References 37610 A Homogenization-Based Prediction Method of Macroscopic Yield Strength of Polycrystalline Metals Subjected to Cold-Working 379Kenjiro Terada, Ikumu Watanabe, Masayoshi Akiyama, Shigemitsu Kimura, and Kouichi Kuroda10.1 Introduction 37910.2 Two-Scale Modeling and Analysis Based on Homogenization Theory 38210.2.1 Two-Scale Boundary Value Problem 38310.2.2 Micro–Macro Coupling and Decoupling Schemes for the Two-Scale BVP 38510.2.3 Method of Evaluating Macroscopic Yield Strength after Cold-Working 38610.3 Numerical Specimens: Unit Cell Models with Crystal Plasticity 38710.4 Approximate Macroscopic Constitutive Models 39010.4.1 Definition of Macroscopic Yield Strength 39110.4.2 Macroscopic Yield Strength at the Initial State 39110.4.3 Approximate Macroscopic Constitutive Model 39310.4.4 Parameter Identification for Approximate Macroscopic Constitutive Model 39310.5 Macroscopic Yield Strength after Three-Step Plastic Forming 39510.5.1 Forming Condition 39510.5.2 Two-Scale Analyses with Micro–Macro Coupling and Decoupling Schemes 39610.5.3 Evaluation of Macroscopic Yield Strength after Three-Step Plastic Forming 39810.6 Application for Pilger Rolling of Steel Pipe 40110.6.1 Forming Condition 40110.6.2 Decoupled Microscale Analysis 40310.6.3 Evaluation of Macroscopic Yield Strength after Pilger Rolling Process 40610.7 Conclusion 408References 409Index 413

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