State of the Art and Future Trends in Material Modeling (eBook)

Preface 6
Contents 8
List of Contributors 18
1On Viscoelasticity in the Theory of Geometrically Linear Plates 26
1.1 Introduction 26
1.1.1 Motivation 26
1.1.2 Organisation of the Paper 27
1.1.3 Preliminaries and Notation 28
1.2 Linear Elastic Background 30
1.3 Constitutive Models for Linear Viscoelasticity 34
1.3.1 Basic Elements of Rheological Circuits 34
1.3.2 Series Arrangement of Elements 36
1.3.3 Parallel Arrangement of Elements 37
1.4 Application to Viscoelastic Plates 37
1.4.1 Maxwell Model 38
1.4.2 Kelvin Model 40
1.4.3 Visualization of Model Behavior 40
1.4.4 Ansatz for Viscous Parameters 41
1.5 Determination of Material Parameters 43
1.6 Conclusion 44
References 46
2Teaching Mechanics 48
2.1 Background 48
2.2 The Development of Mechanics Teaching 50
2.3 A New Conceptual Approach 55
2.4 Teaching Introductory Mechanics 57
2.4.1 Conceptual Misunderstandings in Newtonian Mechanics 58
2.4.2 Kinematics & The Law of Falling Bodies
2.4.3 Basic Forces 59
2.4.4 Connected Bodies, Free Body Diagrams and Problem Solving 62
2.4.5 Using Socratic Dialogue with Technology 63
2.5 More Advanced Topics: Continuum Mechanics 65
2.5.1 Teaching Introductory Statics 65
2.5.2 Introducing Continuum Mechanics 67
2.6 Conclusions 69
References 70
3 Modeling of Damage of Ductile Materials 74
3.1 Introduction 75
3.2 Continuum Damage Model 77
3.2.1 Basic Ideas 77
3.2.2 Thermodynamically Consistent Model 79
3.2.3 Damage Mode Parameters Based on Numerical Simulations on the Micro-scale 83
3.3 Experiments and Corresponding Numerical Simulations 85
3.3.1 Experimental Equipment and Specimens 85
3.3.2 Numerical Aspects 87
3.3.3 Results of Biaxial Experiments and Corresponding Numerical Simulations 88
3.4 Conclusions 100
References 100
4Creep in Heat-resistant Steels at Elevated Temperatures 104
4.1 Introduction 104
4.2 Basics About Creep in Heat-resistant Steels 106
4.2.1 Microstructure of Heat-resistant Steels 106
4.2.2 Definition of Creep and Influence of Stress and Temperature 107
4.2.3 Classical Creep Curve. Primary, Secondary, and Tertiary Creep 109
4.3 Constitutive Modeling of Creep 111
4.3.1 Early Approaches 112
4.3.2 Nonunified Models 114
4.3.3 Unified Models 116
4.4 Constitutive Modeling of Creep Damage 121
4.4.1 Cavity Growth Mechanism Models 122
4.4.2 Continuum Damage Mechanics Models 123
4.5 Conclusion and Outlook 125
References 127
5 Surface Elasticity Models: Comparison Through the Condition of the Anti-plane Surface Wave Propagation 138
5.1 Introduction 138
5.2 Anti-plane Motions of an Elastic Half-Space 139
5.3 Constitutive Relations Within the Surface Elasticity 141
5.3.1 Simplified Linear Gurtin-Murdoch Model 141
5.3.2 Linear Stress-gradient Surface Elasticity 141
5.3.3 Linear Strain-gradient Surface Elasticity 143
5.4 Dispersion Relations 143
5.5 Conclusions 146
References 147
6Anisotropic Material Behavior 150
6.1 Elastic Anisotropy 150
6.1.1 Triclinic Symmetry 151
6.1.2 Monoclinic Symmetry 154
6.1.3 Trigonal/Rhombohedral Symmetry 155
6.1.4 Orthorhombic Symmetry 155
6.1.5 Tetragonal Transverse Isotropy 156
6.1.6 Hexagonal Transverse Isotropy 157
6.1.7 Cubic Symmetry 158
6.2 Plastic Anisotropy 158
6.2.1 Goldenblat–Kopnov’s Criterion 159
6.2.2 Von Mises’ Anisotropic Criterion 160
6.2.3 Von Mises’ Orthotropic Criterion and Hill’s Deviatoric Criterion 165
6.2.4 Barlat–Khan’s Implicit Formulations 169
6.2.5 Brief Survey of Anisotropic Yield Criteria 172
References 174
7Coupled Problems in Thermodynamics 176
7.1 Introduction 176
7.2 Historical Remarks and the State of the Art 178
7.2.1 Preliminary Remarks 178
7.2.2 Statistical Thermodynamics and Continuum Mechanics 178
7.2.3 Non-equilibrium Thermodynamics and Continuum Mechanics 181
7.2.4 A Brief Overview of Current Research 183
7.3 Mechanical Models for Studying Coupled Problems in Thermodynamics 185
7.3.1 Preliminary Remarks 185
7.3.2 The Cosserat Continuum of Special Type 185
7.3.3 Mechanical Analogies of Physical Quantities 188
7.3.4 Simulating Thermodynamic and Electromagnetic Processes in Matter 188
7.3.5 Analysis of the Wave Behavior at the Interface 190
7.4 Whether Modern Thermodynamics Needs Mechanical Models 194
References 194
8Estimation of Energy of Fracture Initiation in Brittle Materials with Cracks 198
8.1 Introduction 198
8.2 Discrete Model of a Brittle Material 200
8.3 An Infinite Rectangular Crack 201
8.4 A Penny-shaped Crack 203
8.5 Multiple Randomly Oriented Penny-shaped Cracks (Non-interaction Approximation) 204
8.6 Conclusions 204
References 205
9Effective Elastic Properties Using Maxwell’s Approach for Transversely Isotropic Composites 208
9.1 Introduction 209
9.2 Statement of Fundamental Equations 211
9.3 Geometry of Inclusions 213
9.4 Maxwell’s Homogenization Approach 215
9.5 Analysis of Numerical Results 217
9.5.1 Density Distribution Functions 218
9.5.2 Study of Composites Constituted by Isotropic Matrix and Isotropic Inhomogeneities 219
9.5.3 Study of Composites Constituted by Isotropic Matrix and Transversely Isotropic Inhomogeneities 223
9.5.5 Two-phase Nano-composites 227
9.6 Conclusions 227
Appendix 228
References 233
10Advanced Numerical Models for Predicting the Load and Environmentally Dependent Behaviour of Adhesives and Adhesively Bonded Joints 236
10.1 Introduction 237
10.2 Modelling Adhesives and Adhesive Joints Using Cohesive Zone Models and Extended Finite Element Method 238
10.3 Modelling of Adhesives and Adhesive Joints Under Varying Loading Rates and Impact Conditions 243
10.4 Modelling the Behaviour of Adhesives and Adhesive Joints Under Hygrothermal Ageing Conditions 247
10.5 Modelling of Adhesives and Adhesive Joints Under Cyclic Loads 255
References 264
11A Short Review of Electromagnetic Force Models for Matter - Theory and Experimental Evidence 270
11.1 Compilation of Relevant Force Models 270
11.2 Intermezzo 272
11.3 Case I: Magnetostriction of a Spherical Permanent Magnet 273
11.4 Case II: Deformation of a Spherical Droplet due to Electric Polarization 275
11.5 Case III: Elastic Deformation of Spherical Electrets due to Electric Polarization and Surface Charges 276
11.6 Case IV: Force and Torque Interaction Between Spherical Magnets 279
11.7 Conclusions and Outlook 282
References 282
12Extreme Yield Figures for Universal Strength Criteria 284
12.1 Introduction 285
12.2 Requirements for Yield Criteria 286
12.3 Formulating Yield Criteria 287
12.4 Comparing Different Yield Criteria 289
12.4.1 Geometry of Limit Surfaces in the ?-plane 290
12.4.2 Material Properties and Basic Experiments 293
12.5 Extreme Yield Figures 294
12.6 Generalized Strength Criteria 296
12.6.1 Modified Yu Strength Criterion 298
12.6.2 Podgórski Criterion 298
12.6.3 Modified Altenbach-Zolochevsky Criterion 300
12.6.4 Universal Yield Criterion of Trigonal Symmetry 301
12.6.5 Universal Deviatoric Function 308
12.7 Application to Concrete 313
12.7.1 Objective Functions 313
12.7.2 Approximation and Restrictions 314
12.7.3 Comparison of Approximations 317
12.8 Summary 327
Appendices 328
A.1 Invariants of the Stress Tensor 328
A.2 Geometric Properties in the ?-plane 330
A.3 Identification of Limit Surface for Pressure-sensitive Materials 331
A.4 Derivation of the Modified Yu Strength Criterion 333
A.5 Properties of the Podgórski Criterion 335
A.6 Properties of the Modified Altenbach-Zolochevsky Criterion 336
A.7 Measured Concrete Data 337
A.8 Estimates and Parameter Studies 337
References 338
13On the Derivation and Application of a Finite Strain Thermo-viscoelastic Material Model for Rubber Components 350
13.1 Introduction 350
13.2 Elastomer Structure and Behaviour 352
13.3 Continuum Mechanical Material Modelling 353
13.3.1 Balance Equations 354
13.3.2 Quasi-incompressible Modified Thermoviscoelasticity 356
13.3.3 Heat Conduction Equation 359
13.4 Finite Element Implementation 360
13.5 Material Model 364
13.6 Model Validation 367
13.6.1 Parameter Identification 368
13.6.2 Computational Model 369
13.6.3 Analysis 369
13.7 Summary and Conclusion 371
References 372
14Additive Manufacturing: A Review of the Influence of Building Orientation and Post Heat Treatment on the Mechanical Properties of Aluminium Alloys 374
14.1 Nomenclatur 375
14.2 Introduction 375
14.3 Additive Manufacturing - Selective Laser Melting 376
14.4 Mechanical Properties 377
14.4.1 Hardness 379
14.4.2 Tensile Strength 383
14.5 Conclusions 387
References 388
15Efficient Numerics for the Analysis of Fibre-reinforced Composites Subjected to Large Viscoplastic Strains 392
15.1 Introduction 392
15.2 Material Model of the Fibre-reinforced Composite 393
15.2.1 Isotropic Viscoplasticity for the Matrix 394
15.2.2 Anisotropic Viscoplasticity for the Fibre 395
15.3 Efficient Numerics 397
15.3.1 Isotropic Viscoplasticity of the Matrix 397
15.3.2 Anisotropic Viscoplasticity of the Fibre 399
15.4 Tests and Applications 401
15.4.1 Single Fibre 401
15.4.2 Inflation of a Viscoplastic Composite Tube 402
15.5 Discussion and Conclusion 404
References 404
16An Artificial Intelligence-based Hybrid Method for Multi-layered Armour Systems 406
16.1 Introduction 407
16.1.1 The Hybrid Methodology 407
16.2 Plugging of Ductile Plates: Analytical Modelling 408
16.3 Plugging of Ductile Plates: Neural Network Model 411
16.3.1 Training Process 412
16.3.2 Problem Setting 414
16.3.3 Artificial Intelligence Setup 415
16.4 Results and Discussion 417
16.4.1 Finite Element Modelling 420
16.5 Conclusions and Final Remarks 422
References 423
17A Review on Numerical Analyses of Martensitic Phase Transition in Mono and Polycrystal Transformation-induced Plasticity Steel by Crystal Plasticity Finite Element Method with Length Scales 426
17.1 Introduction 427
17.2 Literature Survey of Problems on Length Scales Regarding with Martensitic Phase Transformation 429
17.2.1 Effects of Length Scales in the Parent Phase 429
17.2.2 Effects of Length Scales in the Product Phase 431
17.3 Computational Aspects 432
17.3.1 A Model of Single Crystal Transformation-induced Plasticity Steel Based on Continuum Crystal Plasticity Suggested by Iwamoto and Tsuta (2004) 433
17.3.2 Computational Models and Conditions for Single and Polycrystal Transformation-induced Plasticity Steel 434
17.4 Computational Results and Discussions 436
17.4.1 Effect of Mesh Discritization for Single Crystal Transformation-induced Plasticity Steel 436
17.4.2 Polycrystal Transformation-induced Plasticity Steel 438
17.5 Summary 442
References 442
18On Micropolar Theory with Inertia Production 446
18.1 Introduction 446
18.2 Outline of the Theory 450
18.3 Special Cases for the Production Term 454
18.3.1 Milling Matter in a Crusher 454
18.3.2 Turning Heat Conduction into Space-varying Rotational Motion 458
18.3.3 Dipolar Polarization 461
18.4 Conclusions and Outlook 463
References 465
19Hencky Strain and Logarithmic Rate for Unified Approach to Constitutive Modeling of Continua 468
19.1 Introduction 469
19.2 Hencky Invariants and Rubber-like Elasticity 470
19.2.1 Modeling of Rubber-like Elasticity 470
19.2.2 Direct Potential with Hencky Strain 471
19.2.3 Bridging Invariants and Mode Invariant 472
19.2.4 Elastic Potentials Automatically Reproducing Uniaxial and Biaxial Responses 473
19.2.5 Elastic Potentials Automatically Reproducing both Uniaxial and Plane-strain Responses 475
19.3 Self-consistent Prandtl-Reuss Equations with Log-rate 476
19.3.1 Prandtl-Reuss Equations with Objective Rates 477
19.3.2 Inconsistency Issues with Zaremba-Jaumann Rate 479
19.3.3 Self-consistent Formulation with Log-rate 480
19.3.4 Remarks on Recently Raised Issues 482
19.4 Log-rate-based Elastoplastic J2?flow Equations for Shape Memory Alloy Pseudo-elasticity 487
19.5 Log-rate-based Elastoplastic Equations for Shape Memory Effects 489
19.5.1 Log-rate-based Elastoplastic Equations with Thermal Effects 489
19.5.2 Plastic Flow Induced at Pure Heating 490
19.5.3 Recovery Effect 491
19.5.4 Further Results 492
19.6 Innovative Elastoplastic Equations Automatically Incorporating Failure Effects 493
19.6.1 New Elastoplastic Constitutive Equations 494
19.6.2 A Criterion for Critical Failure States 495
19.6.3 Full-strain-range Response up to Failure 496
19.6.4 Failure Effects Under Various Stress Amplitudes 496
19.7 Deformable Micro-continua for Quantum Entities at Atomic Scale 498
19.7.1 The Quantum-continua 498
19.7.2 Continuity Equation and Balance Equations 499
19.7.3 Constitutive Equation for Deformability Nature 500
19.7.4 Inherent Response Features of the Quantum-continua 500
19.7.5 New Patterns for Hydrogen Atom as Quantum-continuum 501
19.7.6 New Insight into the Uncertainty Principle 503
19.7.7 Remarks 505
19.8 Concluding Remarks 505
References 506
20A Multi-disciplinary Approach for Mechanical Metamaterial Synthesis: A Hierarchical Modular Multiscale Cellular Structure Paradigm 510
20.1 Introduction 511
20.2 Synergistic Approach for Metamaterial Synthesis and Fabrication 517
20.3 Digital Image Correlation-based Metamaterial Design Process 519
20.4 Preliminary Results 521
20.5 Conclusion 523
References 524