From Microstructure Investigations to Multiscale Modeling

Delphine Brancherie is Associate Professor in the Department of Mechanical Engineering at the University of Technology of Compiegne, France. Her research works fit into the field of computational mechanics with a particular interest in modeling inelastic materials until rupture.Pierre Feissel is Professor in the Department of Mechanical Engineering at the University of Technology of Compiegne, France. His research work is dedicated to the bridging between computational and experimental mechanics, with a particular interest in the treatment of uncertainty.Salima Bouvier is Professor in the Department of Mechanical Engineering at the University of Technology of Compiegne, France. Her research fields include scale transition in metallic materials from an experimental point of view to constitutive modeling.Adnan Ibrahimbegovic is Professor at the University of Technology of Compiegne, France. He is recognized for his works in the field of computational mechanics, including multibody dynamics, continuum and discrete models for fracture, multiscale modeling of inelastic behavior and coupled problems.

• Preface xiChapter 1. Synchrotron Imaging and Diffraction for In Situ 3D Characterization of Polycrystalline Materials 1Henry PROUDHON1.1. Introduction 11.2. 3D X-ray characterization of structural materials 31.2.1. Early days of X-ray computed tomography 31.2.2. X-ray absorption and Beer Lambert’s law 41.2.3. X-ray detection 61.2.4. Radon’s transform and reconstruction 81.2.5. Synchrotron X-ray microtomography 101.2.6. Phase contrast tomography 131.2.7. Diffraction contrast tomography 141.3. Nanox: a miniature mechanical stress rig designed for near-field X-ray diffraction imaging techniques 161.4. Coupling diffraction contrast tomography with the finite-element method. 191.4.1. Motivation for image-based mechanical computations 191.4.2. 3D mesh generation from tomographic images 201.4.3. Toward a fatigue model at the scale of the polycrystal 281.5. Conclusion and outlook 291.6. Bibliography 31Chapter 2. Determining the Probability of Occurrence of Rarely Occurring Microstructural Configurations for Titanium Dwell Fatigue 41Adam L. PILCHAK, Joseph C. TUCKER and Tyler J. WEIHING2.1. Introduction 422.2. Experimental methods 442.2.1. MTR quantification metrics 442.2.2. Synthetic microstructure generation 462.2.3. Crystallographic analysis for titanium dwell fatigue 482.2.4. Block maxima 502.3. Results and discussion 512.3.1. Probability of occurrence 532.3.2. “Hard” MTR size distributions 572.3.3. Block maxima 582.4. Summary and outlook 632.5. Bibliography 64Chapter 3. Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities 67Hilal REDA, Yosra RAHALI, Jean-François GANGHOFFER and Hassan LAKISS3.1. Introduction 683.2. Extensible energy of pantograph for dynamic analysis 703.2.1. Expression of the pantographic network energy 703.2.2. Dynamic equilibrium equation 733.3. Wave propagation in a nonlinear elastic beam 753.3.1. Legendre–Hadamard ellipticity condition and loss of stability 773.3.2. Supersonic and subsonic modes for 1D wave propagation 783.3.3. Wave dispersion relation in 2D nonlinear periodic structures 813.3.4. Anisotropic behavior of 2D pantographic networks versus the degree of nonlinearity 843.4. Conclusion 853.5. Appendix 863.6. Bibliography 94Chapter 4. Multiscale Model of Concrete Failure 99Emir KARAVELIĆ, Mijo NIKOLIĆ and Adnan IBRAHIMBEGOVIĆ4.1. Introduction 994.2. Meso-scale model 1024.3. Macroscopic model response 1064.3.1. Uniaxial tests 1064.3.2. Failure surface 1114.4. Conclusions 1174.5. Acknowledgments 1194.6. Bibliography 120Chapter 5. Discrete Numerical Simulations of the Strength and Microstructure Evolution During Compaction of Layered Granular Solids 123Bereket YOHANNES, Marcial GONZALEZ and Alberto M. CUITIÑO5.1. Introduction 1235.2. Numerical simulation 1275.2.1. Discrete particle simulations of powder compaction 1275.2.2. Discrete particle simulation of layered compacts 1295.3. Discussion 1315.4. Conclusion 1375.5. Acknowledgements 1375.6. Bibliography 137Chapter 6. Microstructural Views of Stresses in Three-Phase Granular Materials 143Jérôme DURIEZ, Richard WAN and Félix DARVE6.1. Microstructural expression of triphasic total stresses 1456.1.1. Stress description within micro-scale volumes and interfaces of triphasic materials 1456.1.2. Total stress derivation 1466.2. Numerical modeling of wet ideal granular materials 1496.2.1. DEM description of fluid microstructure 1496.2.2. DEM description of stress and strains 1526.3. Anisotropy of the capillary stress contribution 1546.3.1. Mechanical loading 1556.3.2. Hydraulic loading 1576.4. Effective stress 1606.5. Conclusion 1626.6. Bibliography 163Chapter 7. Effect of the Third Invariant of the Stress Deviator on the Response of Porous Solids with Pressure-Insensitive Matrix 167José Luis ALVES and Oana CAZACU7.1. Introduction 1687.2. Problem statement and method of analysis 1717.2.1. Drucker yield criterion for isotropic materials 1717.2.2. Unit cell model 1737.3. Results 1797.3.1. Yield surfaces and porosity evolution 1797.4. Conclusions 1907.5. Bibliography 194Chapter 8. High Performance Data-Driven Multiscale Inverse Constitutive Characterization of Composites 197John MICHOPOULOS, Athanasios ILIOPOULOS, John HERMANSON, John STEUBEN and Foteini KOMNINELI8.1. Introduction 1988.2. Automated multi-axial testing 2028.2.1. Loading space 2048.2.2. Experimental campaign 2068.3. Constitutive formalisms 2078.3.1. Small strain formulation 2088.3.2. Finite strain formulation 2098.4. Meshless random grid method for experimental evaluation of strain fields 2098.5. Inverse determination of HDM via design optimization 2118.5.1. Numerical results of design optimization 2148.6. Surrogate models for characterization 2168.6.1. Definition and construction of the surrogate model 2188.6.2. Characterization by optimization 2198.6.3. Validation with physical experiments 2218.7. Multi-scale inversion 2218.7.1. Forward problem: mathematical homogenization 2228.7.2. Inverse problem 2248.8. Computational framework and synthetic experiments 2268.9. Conclusions and plans 2308.10. Acknowledgments 2328.11. Bibliography 232Chapter 9. New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data-Driven 239Jose Vicente AGUADO, Domenico BORZACCHIELLO, Elena LOPEZ, Emmanuelle ABISSET-CHAVANNE, David GONZALEZ, Elias CUETO and Francisco CHINESTA9.1. Introduction 2409.1.1. The big picture 2409.1.2. The PGD at a glance 2429.2. Constructing slow manifolds 2459.2.1. From principal component analysis (PCA) to kernel principal component analysis (kPCA) 2459.2.2. Kernel principal component analysis (kPCA) 2499.2.3. Locally linear embedding (LLE) 2509.2.4. Discussion 2519.3. Manifold-learning-based computational mechanics 2529.4. Data-driven simulations 2539.4.1. Data-based weak form 2549.4.2. Constructing the constitutive manifold 2549.5. Data-driven upscaling of viscous flows in porous media 2579.5.1. Upscaling Newtonian and generalized Newtonian fluids flowing in porous media 2589.6. Conclusions 2609.7. Bibliography 261List of Authors 267Index 271