Title Details

Preface xi

Chapter 1 Synchrotron Imaging and Diffraction for In Situ 3D Characterization of PolycrystallineMaterials 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 MechanicalInstabilities 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 KARAVELIÆ, Mijo NIKOLIÆ and Adnan IBRAHIMBEGOVIÆ

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 DuringCompaction 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 withPressure-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 Composites197
John MICHOPOULOS, Athanasios ILIOPOULOS, John HERMANSON, John STEUBEN and FoteiniKOMNINELI

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