Mechanics and Physics of Solids at Micro- and Nano-Scales

Introduction xi

Part 1. Plastic Deformation of Crystalline Materials 1

Chapter 1. Homogeneous Dislocation Nucleation in Landau Theory of Crystal Plasticity 3
Oguz Umut SALMAN and Roberta BAGGIO

1.1. Introduction 3

1.2. The model 6

1.2.1. Linear stability analysis 9

1.3. Numerical implementation 11

1.4. Simulation results 12

1.4.1. Stress field of a single-edge dislocation 12

1.4.2. Dislocation annihilation 13

1.4.3. Homogeneous nucleation 14

1.5. Conclusion 18

1.6. References 18

Chapter 2. Effects of Rate, Size, and Prior Deformation in Microcrystal Plasticity 25
Stefanos PAPANIKOLAOU and Michail TZIMAS

2.1. Introduction 25

2.2. Model 27

2.3. Effects of loading rates and protocols in crystal plasticity 29

2.4. Size effects in microcrystal plasticity 36

2.5. Unveiling the crystalline prior deformation history using unsupervised machine learning approaches 38

2.6. Predicting the mechanical response of crystalline materials using supervised machine learning 43

2.7. Summary 48

2.8. Acknowledgements 49

2.9. References 49

Chapter 3. Dislocation Dynamics Modeling of the Interaction of Dislocations with Eshelby Inclusions 55
Sylvie AUBRY, Sylvain QUEYREAU and Athanasios ARSENLIS

3.1. Introduction 55

3.2. Review of existing approaches 57

3.2.1. Modeling discrete precipitates with DD simulations 57

3.2.2. Investigation of precipitation strengthening and some related effects 61

3.3. Dislocation dynamics modeling of dislocation interactions with Eshelby inclusions 63

3.3.1. Stress field and forces at dislocation lines 63

3.3.2. Stress at a point induced by an inclusion 64

3.3.3. Force on a dislocation coming from an inclusion 64

3.3.4. Far field interactions induced by an Eshelby inclusion 68

3.3.5. Parallel implementation 68

3.4. DD simulations of the interaction with Eshelby inclusions 69

3.4.1. Eshelby force for a single dislocation and a single inclusion 69

3.4.2. Simulations of bulk crystal plasticity 70

3.5. Conclusion and discussion 77

3.6. Acknowledgments 79

3.7. Appendix: derivation of the Eshelby force 80

3.8. References 82

Chapter 4. Scale Transition in Finite Element Simulations of Hydrogen–Plasticity Interactions 87
Yann CHARLES, Hung Tuan NGUYEN, Kevin ARDON and Monique GASPERINI

4.1. Introduction 87

4.2. Modeling assumptions 92

4.2.1. Crystal plasticity mechanical behavior 92

4.2.2. Hydrogen transport equation 93

4.2.3. Implementation 95

4.2.4. Mechanical parameters 96

4.3. Identification of a trap density function at the crystal scale 97

4.3.1. Geometry, mesh, and boundary conditions applied on the polycrystals 98

4.3.2. Results 100

4.4. Adaptation of the Dadfarnia’s model at the crystal scale 104

4.4.1. Formulation at the polycrystal scale 104

4.4.2. Application to single crystals 106

4.4.3. Boundary and initial conditions 107

4.4.4. Crystal orientations 108

4.4.5. Results 108

4.4.6. Consequences on hydrogen transport through a polycrystalline bar 113

4.5. Conclusion 118

4.6. Appendix: Numbering of the slip systems in the UMAT 118

4.7. References 119

Part 2. Mechanics and Physics of Soft Solids 131

Chapter 5. Compression of Fiber Networks Modeled as a Phase Transition 133
Prashant K. PUROHIT

5.1. Introduction 133

5.2. Experimental observations in compressed fibrin clots and CNT forests 134

5.2.1. Compression of platelet-poor plasma clots and platelet-rich plasma clots 134

5.2.2. Compression of CNT forests coated with alumina 138

5.3. Theoretical model based on continuum theory of phase transitions 141

5.3.1. Compression of PPP and PRP clots 141

5.3.2. Phase transition theory 143

5.3.3. Effect of liquid pumping 145

5.3.4. Application of phase transition model to PPP and PRP clots 146

5.3.5. Predictive capability of our model 148

5.3.6. Application of phase transition model to CNT networks 148

5.4. Conclusion 151

5.5. References 153

Chapter 6. Mechanics of Random Networks of Nanofibers with Inter-Fiber Adhesion 157
Catalin R. PICU and Vineet NEGI

6.1. Introduction 157

6.2. Mechanics in the presence of adhesion 160

6.2.1. The adhesive interaction of two fibers 160

6.2.2. Triangle of fiber bundles 163

6.3. Structure of non-crosslinked networks with inter-fiber adhesion 165

6.4. Tensile behavior of non-crosslinked networks with inter-fiber adhesion 169

6.5. Structure of networks with inter-fiber adhesion and crosslinks 171

6.6. Tensile behavior of crosslinked networks with inter-fiber adhesion 173

6.7. Conclusion 179

6.8. References 180

Chapter 7. Surface Effects on Elastic Structures 185
Hadrien BENSE, Benoit ROMAN and José BICO

7.1. Introduction 185

7.2. Liquid surface energy 186

7.2.1. Can a liquid deform a solid? 186

7.2.2. Slender structures 187

7.2.3. Wrapping a cylinder 188

7.2.4. Capillary origamis 190

7.3. Dielectric elastomers: a surface effect? 192

7.3.1. Introduction: electrostatic energy of a capacitor as a surface energy 192

7.3.2. Mechanics of dielectric elastomers 194

7.3.3. Buckling experiments 202

7.4. Conclusion 209

7.5. References 210

Chapter 8. Stress-driven Kirigami: From Planar Shapes to 3D Objects 215
Alexandre DANESCU, Philippe REGRENY, Pierre CRÉMILIEU and Jean-Louis LECLERCQ

8.1. Introduction 215

8.2. Bilayer plates with pre-stress 216

8.3. Constant curvature ribbons and geodesic curvature 219

8.3.1. Experimental evidence 220

8.3.2. Geodesic objects 222

8.4. Directional bending of large surfaces 223

8.4.1. Photonic crystals tubes 224

8.4.2. Control the directional bending 225

8.5. Conclusion 227

8.6. References 227

Chapter 9. Modeling the Mechanics of Amorphous Polymer in the Glass Transition 231
Hélène MONTES, Aude BELGUISE, Sabine CANTOURNET and François LEQUEUX

9.1. Introduction 231

9.2. Modeling the mechanics of amorphous 233

9.2.1. Input physics 233

9.2.2. Temperature dependence of the intrinsic relaxation times 235

9.2.3. Length scales in the model 236

9.2.4. Numerical implementation 237

9.3. Linear regime in bulk geometry 239

9.3.1. Stress relaxation 239

9.3.2. Numerical predictions versus experiments in the linear regime 240

9.3.3. Role of elastic coupling between domains 241

9.4. Linear regime in confined geometries 244

9.4.1. Apparent linear viscoelasticity in various geometries 244

9.4.2. Comparison of the results of our model with the observation of Tg shift in filled elastomers 247

9.4.3. Role of mechanical coupling in confined geometry 250

9.4.4. Conclusion on the effects of confinement 252

9.5. Nonlinear mechanics 253

9.5.1. Input of nonlinearities 254

9.5.2. Results of the model 255

9.5.3. Role of elastic coupling in the nonlinear regime 256

9.6. Conclusion 257

9.7. Appendix 258

9.8. References 259

List of Authors 263

Index 267