Virtual Design and Validation (eBook)

Preface 6
Contents 8
Experiments and Virtual Design 10
Digital Volume Correlation of Laminographic and Tomographic Images: Results and Challenges 11
1 Introduction 11
2 Challenges 12
2.1 Material Microstructure 12
2.2 CT Imaging and Artifacts 13
2.3 Volume of Data/Duration of Acquisition 13
2.4 Detecting Features Invisible to the Eye 14
3 Recent Solutions 15
3.1 Filtering 3D Images 15
3.2 Global DVC 16
3.3 Reduced Bases and Integrated DVC 18
3.4 Regularized DVC 21
3.5 Projection-Based DVC 23
4 Conclusion 24
References 24
Manufacturing and Virtual Design to Tailor the Properties of Boron-Alloyed Steel Tubes 29
1 Introduction 30
2 Material 31
3 Technological Process 32
4 Phase Transformations During Heat-Treatment 33
4.1 Austenite Formation During Inductive Heating 33
4.2 Austenite Decomposition During Spray Cooling 39
5 Non-destructive Microstructure Characterization 43
6 Virtual Design of Tube Heat-Treatment 47
7 Conclusions 49
References 50
Mathematical Modelling and Analysis of Temperature Effects in MEMS 53
1 Introduction 53
2 The Full Model 55
2.1 The Evolution of the Membrane 56
2.2 The Electrostatic Potential 57
2.3 The Temperature 58
2.4 Transformation of the System 60
2.5 Examples for the Temperature Dependence 61
3 The Small Aspect Ratio Limit 62
3.1 The System 63
3.2 Solution to the Thermal and Electrostatic Problems 63
3.3 Well-Posedness of the Deflection Problem 64
References 66
Multi-fidelity Metamodels Nourished by Reduced Order Models 68
1 Introduction 69
2 Multi-fidelity Kriging in a Nutshell 70
3 Presentation of the Mechanical Problem and the LATIN Solver 72
3.1 Mechanical Problem 72
3.2 Chaboche's Elasto-Viscoplastic Behavior Law 72
3.3 LATIN-PGD Solver 74
4 Presentation of the Test-Cases 75
4.1 Test-Case 1: Plate with Inclusion 76
4.2 Test-Case 2 : Damping Part 77
5 Implementation of the Coupling Strategy 78
5.1 Correlation Between Error on the Quantity of Interest and LATIN Error Indicator 78
5.2 Method Used for Test Campaigns 79
6 Results of the Test Campaign 80
6.1 Full Generation of the Metamodel—Test-Case 1 80
6.2 Full Generation of the Metamodel—Test-Case 2 82
6.3 EGO Method for Finding the Global Optimum—Test-Case 1 82
6.4 EGO Method for Finding the Global Optimum - Test-Case 2 84
7 Conclusion 85
References 85
Application of Enhanced Peridynamic Correspondence Formulationpg for Three-Dimensional Simulationspg at Large Strains 87
1 Introduction 87
2 General Framework 88
3 Correspondence Formulation 91
3.1 Meshfree Discretisation 91
3.2 Time Integration 92
3.3 Stability Problems 93
3.4 Enhanced Formulation 94
4 Numerical Examples 96
4.1 Tension of a Rod 97
4.2 Punch Test 100
4.3 Torsion of Rod 105
5 Conclusion 108
References 109
Isogeometric Multiscale Modeling with Galerkin and Collocation Methods 111
1 Introduction 111
2 Basis Functions 113
2.1 B-Splines 114
2.2 Non-uniform Rational B-Splines 114
3 Computational Homogenization 115
3.1 Macroscopic Equilibrium Problem 115
3.2 Microscopic Equilibrium Problem 115
4 Isogeometric Formulation 116
4.1 Isogeometric Galerkin Formulation 116
4.2 Isogeometric Collocation Formulation 118
5 Numerical Examples 119
5.1 Microscale Problem 119
6 Conclusion 124
References 125
Composites 127
Experimental and Numerical Investigations on the Combined Forming Behaviour of DX51 and Fibre Reinforced Thermoplastics Under Deep Drawing Conditions 128
1 Introduction 129
2 Methodology 132
2.1 Experimental Procedure 133
2.2 Forming Tests 136
2.3 Numerical Methods 136
3 Results and Discussion 138
3.1 Material Characterization and Modelling 138
3.2 Hemispherical Dome Tests 146
4 Summary and Outlook 149
References 149
The Representation of Fiber Misalignment Distributions in Numerical Modeling of Compressive Failure of Fiber Reinforced Polymers 152
1 Introduction 152
1.1 Previous Work 153
1.2 Current Work 155
2 Measurement Data Driven Model Generation 155
2.1 Fiber Misalignment Distribution Generation from Experimentally Characterized Spectral Density 156
2.2 Generated Distributions Examples 163
2.3 Mapping of Fiber Misalignment Distribution to Numerical Model 166
3 Numerical Example Results 168
4 Concluding Remarks 169
References 170
A Multiscale Projection Method for the Analysis of Fiber Microbuckling in Fiber Reinforced Composites 172
1 Introduction 172
2 Fine Scale Modeling 174
3 Transversely Isotropic Material Model for the Coarse Scale 175
4 Geometrically Nonlinear Cohesive Element 176
4.1 Weak Formulation and Kinematics 177
4.2 Finite Element Discretization 178
5 Multiscale Modeling 179
6 Numerical Examples 183
7 Conclusion 187
References 188
Topology Optimization of 1-3 Piezoelectric Composites 190
1 Introduction 190
2 Constitutive Relation of the 1-3 Piezocomposite 192
3 Materials Microstructure Topology Optimization by the Level Set Method 194
4 Optimization Algorithm 197
5 Results 198
6 Conclusion 200
References 201
Fracture and Fatigue 204
Treatment of Brittle Fracture in Solids with the Virtual Element Method 205
1 Introduction 205
2 Governing Equations of Brittle Fracture 207
2.1 Basic Equations of Elastic Body 207
2.2 Crack Propagation Based on Stress Intensity Factors 209
2.3 Phase-Field Approach for Brittle Crack Propagation 211
3 Formulation of the Virtual Element Method 213
3.1 Ansatz Functions for VEM 214
3.2 Residual and Stiffness Matrix of the Virtual Elements 216
4 Construction of the Crack Path 219
5 Numerical Examples 221
5.1 Crack Propagation Using Phase-Field Approach 221
5.2 Crack Propagation Using Stress Intensity Factors 226
6 Conclusion 228
References 229
A Semi-incremental Scheme for Cyclic Damage Computations 233
1 Introduction 233
1.1 Notation 235
2 An Overview of the LATIN-PGD Method 236
2.1 Local Stage 237
2.2 Global Stage 238
3 Variable Amplitude and Frequency Loading 240
3.1 Hybrid Search Direction Formulation 241
4 Optimality of the Generated ROB 242
4.1 Randomised Singular Value Decomposition (RSVD) Compression of PGD Bases 242
5 Numerical Results 243
5.1 Model Verification 244
5.2 Comparison Between Deterministic and Randomised SVD Schemes 245
5.3 Variable Amplitude and Frequency Loading 246
6 Conclusions 249
References 249
Robust Contact and Friction Model for the Fatigue Estimate of a Wire Rope in the Mooring Line of a Floating Offshore Wind Turbine 252
1 Introduction 253
2 Detailed Wire Rope Model 254
2.1 A New Contact and Friction Element for Wire Rope 254
2.2 Comparison to Analytical and Surface to Surface Solutions 257
2.3 Boundary Conditions 260
2.4 Wire Rope Properties 263
3 Application to a FOWT Model 263
3.1 Global Hydrodynamic FOWT Model 263
3.2 Global Model Results 266
3.3 Results of the Detailed Wire Rope Model 267
4 Conclusion 271
References 272
Micromechanically Motivated Model for Oxidation Ageing of Elastomers 274
1 Introduction 274
2 Current State of the Art 276
3 Network Degradation Dynamics 279
3.1 Compartment Model 280
3.2 Reduction Factor 282
4 Continuum Model 284
4.1 Primary Network Stress 285
4.2 Secondary Network Stress 286
4.3 Kirchhoff Stress and Material Tangent 287
5 Numerical Results 288
5.1 Stress Softening and Stiffening 288
5.2 Network Degradation and Permanent Set 289
5.3 Finite Element Example 291
6 Conclusion 292
References 292
Uncertainty Quantification 294
A Bayesian Approach for Uncertainty Quantification in Elliptic Cauchy Problem 295
1 Introduction 295
2 The Steklov-Poincaré Approach for the Cauchy Problem 296
2.1 Forward and Cauchy Problems in Linear Elasticity 296
2.2 The Steklov-Poincaré Method 298
2.3 Conjugate Gradient and Ritz Values Computation 299
3 Bayesian Inference for the Cauchy Problem 300
3.1 Bayes' Theory and Its Application in the Linear Gaussian Case 300
3.2 Application to the Cauchy Problem 301
4 Reduction by Ritz Modes 302
5 Numerical Example 305
6 Conclusion and Perspectives 308
References 309
On-the-Fly Bayesian Data Assimilation Using Transport Map Sampling and PGD Reduced Models 311
1 Introduction 311
2 Posterior Sampling in Bayesian Data Assimilation 313
2.1 Basics on Bayesian Inference 313
2.2 Transport Map Sampling 314
3 PGD Model Order Reduction in Bayesian Inference 318
3.1 Basics on PGD 318
3.2 Transport Map Sampling with PGD Models 318
4 Illustrative Example 319
4.1 Inference Problem 320
4.2 PGD Solution 321
4.3 Sequential Data Assimilation 321
4.4 Uncertainty Propagation on Outputs of Interest 325
5 Conclusions and Prospects 329
References 329
Stochastic Material Modeling for Fatigue Damage Analysis 331
1 Introduction 331
2 Deterministic Modelling of Fatigue Damage 333
2.1 Material Model 333
2.2 Numerical Approach 334
3 Stochastic Modelling of Fatigue Damage 335
3.1 From a Deterministic to a Stochastic Process 336
3.2 Numerical Properties of the Damage Process 336
3.3 Proposed Diffusion Random Process 337
3.4 Drift Term 337
3.5 Diffusion Term 338
3.6 Introduction of the Stochastic Damage Model in the Finite-Element Framework 339
4 Numerical Example 341
4.1 Influence of the Numerical Parameters on the Stochastic Results 342
4.2 Evolution of Stochastic Fatigue Damage 343
4.3 Virtual S-N Curves 345
5 Summary 348
References 348