From Microstructure Investigations to Multiscale Modeling

Salima Bouvier, University of Technology of Compiègne, France

Preface xi

Chapter 1. Synchrotron Imaging and Diffraction for In Situ 3D Characterization of Polycrystalline Materials 1
Henry PROUDHON

1.1. Introduction 1

1.2. 3D X-ray characterization of structural materials 3

1.2.1. Early days of X-ray computed tomography 3

1.2.2. X-ray absorption and Beer Lambert’s law 4

1.2.3. X-ray detection 6

1.2.4. Radon’s transform and reconstruction 8

1.2.5. Synchrotron X-ray microtomography 10

1.2.6. Phase contrast tomography 13

1.2.7. Diffraction contrast tomography 14

1.3. Nanox: a miniature mechanical stress rig designed for near-field X-ray diffraction imaging techniques 16

1.4. Coupling diffraction contrast tomography with the finite-element method. 19

1.4.1. Motivation for image-based mechanical computations 19

1.4.2. 3D mesh generation from tomographic images 20

1.4.3. Toward a fatigue model at the scale of the polycrystal 28

1.5. Conclusion and outlook 29

1.6. Bibliography 31

Chapter 2. Determining the Probability of Occurrence of Rarely Occurring Microstructural Configurations for Titanium Dwell Fatigue 41
Adam L. PILCHAK, Joseph C. TUCKER and Tyler J. WEIHING

2.1. Introduction 42

2.2. Experimental methods 44

2.2.1. MTR quantification metrics 44

2.2.2. Synthetic microstructure generation 46

2.2.3. Crystallographic analysis for titanium dwell fatigue 48

2.2.4. Block maxima 50

2.3. Results and discussion 51

2.3.1. Probability of occurrence 53

2.3.2. “Hard” MTR size distributions 57

2.3.3. Block maxima 58

2.4. Summary and outlook 63

2.5. Bibliography 64

Chapter 3. Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities 67
Hilal REDA, Yosra RAHALI, Jean-François GANGHOFFER and Hassan LAKISS

3.1. Introduction 68

3.2. Extensible energy of pantograph for dynamic analysis 70

3.2.1. Expression of the pantographic network energy 70

3.2.2. Dynamic equilibrium equation 73

3.3. Wave propagation in a nonlinear elastic beam 75

3.3.1. Legendre–Hadamard ellipticity condition and loss of stability 77

3.3.2. Supersonic and subsonic modes for 1D wave propagation 78

3.3.3. Wave dispersion relation in 2D nonlinear periodic structures 81

3.3.4. Anisotropic behavior of 2D pantographic networks versus the degree of nonlinearity 84

3.4. Conclusion 85

3.5. Appendix 86

3.6. Bibliography 94

Chapter 4. Multiscale Model of Concrete Failure 99
Emir KARAVELIĆ, Mijo NIKOLIĆ and Adnan IBRAHIMBEGOVIĆ

4.1. Introduction 99

4.2. Meso-scale model 102

4.3. Macroscopic model response 106

4.3.1. Uniaxial tests 106

4.3.2. Failure surface 111

4.4. Conclusions 117

4.5. Acknowledgments 119

4.6. Bibliography 120

Chapter 5. Discrete Numerical Simulations of the Strength and Microstructure Evolution During Compaction of Layered Granular Solids 123
Bereket YOHANNES, Marcial GONZALEZ and Alberto M. CUITIÑO

5.1. Introduction 123

5.2. Numerical simulation 127

5.2.1. Discrete particle simulations of powder compaction 127

5.2.2. Discrete particle simulation of layered compacts 129

5.3. Discussion 131

5.4. Conclusion 137

5.5. Acknowledgements 137

5.6. Bibliography 137

Chapter 6. Microstructural Views of Stresses in Three-Phase Granular Materials 143
Jérôme DURIEZ, Richard WAN and Félix DARVE

6.1. Microstructural expression of triphasic total stresses 145

6.1.1. Stress description within micro-scale volumes and interfaces of triphasic materials 145

6.1.2. Total stress derivation 146

6.2. Numerical modeling of wet ideal granular materials 149

6.2.1. DEM description of fluid microstructure 149

6.2.2. DEM description of stress and strains 152

6.3. Anisotropy of the capillary stress contribution 154

6.3.1. Mechanical loading 155

6.3.2. Hydraulic loading 157

6.4. Effective stress 160

6.5. Conclusion 162

6.6. Bibliography 163

Chapter 7. Effect of the Third Invariant of the Stress Deviator on the Response of Porous Solids with Pressure-Insensitive Matrix 167
José Luis ALVES and Oana CAZACU

7.1. Introduction 168

7.2. Problem statement and method of analysis 171

7.2.1. Drucker yield criterion for isotropic materials 171

7.2.2. Unit cell model 173

7.3. Results 179

7.3.1. Yield surfaces and porosity evolution 179

7.4. Conclusions 190

7.5. Bibliography 194

Chapter 8. High Performance Data-Driven Multiscale Inverse Constitutive Characterization of Composites 197
John MICHOPOULOS, Athanasios ILIOPOULOS, John HERMANSON, John STEUBEN and Foteini KOMNINELI

8.1. Introduction 198

8.2. Automated multi-axial testing 202

8.2.1. Loading space 204

8.2.2. Experimental campaign 206

8.3. Constitutive formalisms 207

8.3.1. Small strain formulation 208

8.3.2. Finite strain formulation 209

8.4. Meshless random grid method for experimental evaluation of strain fields 209

8.5. Inverse determination of HDM via design optimization 211

8.5.1. Numerical results of design optimization 214

8.6. Surrogate models for characterization 216

8.6.1. Definition and construction of the surrogate model 218

8.6.2. Characterization by optimization 219

8.6.3. Validation with physical experiments 221

8.7. Multi-scale inversion 221

8.7.1. Forward problem: mathematical homogenization 222

8.7.2. Inverse problem 224

8.8. Computational framework and synthetic experiments 226

8.9. Conclusions and plans 230

8.10. Acknowledgments 232

8.11. Bibliography 232

Chapter 9. New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data-Driven 239
Jose Vicente AGUADO, Domenico BORZACCHIELLO, Elena LOPEZ, Emmanuelle ABISSET-CHAVANNE, David GONZALEZ, Elias CUETO and Francisco CHINESTA

9.1. Introduction 240

9.1.1. The big picture 240

9.1.2. The PGD at a glance 242

9.2. Constructing slow manifolds 245

9.2.1. From principal component analysis (PCA) to kernel principal component analysis (kPCA) 245

9.2.2. Kernel principal component analysis (kPCA) 249

9.2.3. Locally linear embedding (LLE) 250

9.2.4. Discussion 251

9.3. Manifold-learning-based computational mechanics 252

9.4. Data-driven simulations 253

9.4.1. Data-based weak form 254

9.4.2. Constructing the constitutive manifold 254

9.5. Data-driven upscaling of viscous flows in porous media 257

9.5.1. Upscaling Newtonian and generalized Newtonian fluids flowing in porous media 258

9.6. Conclusions 260

9.7. Bibliography 261

List of Authors 267

Index 271