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

Ioan R. Ionescu is Professor at University Paris 13 and at LSPM (Laboratory of Processes and Materials Sciences) of CNRS, Villetaneuse, France. His research focuses on computational solid-mechanics, damage, plasticity, friction and solid-Earth geophysics. Sylvain Queyreau is Associate Professor at University Paris 13 with a CNRS Chair of Excellence at LSPM. His research focuses on atomic and mesoscopic simulations of the plastic behavior, microstructural evolution and fracture initiation in crystalline materials. Catalin R. Picu is Professor and Associate Head of Undergraduate Studies in Mechanical, Aerospace and Nuclear Engineering at Rensselaer Polytechnic Institute, Troy, New York. His research focuses on mechanics and solids, micro- and nano-mechanics of crystalline defects and atomistic simulations. Oguz Umut Salman is a CNRS Researcher at LSPM and a Lecturer at University Paris 13. His research focuses on materials science, plasticity, fractures, phase transitions and bio-mechanics.

• Introduction xiPart 1. Plastic Deformation of Crystalline Materials 1Chapter 1. Homogeneous Dislocation Nucleation in Landau Theory of Crystal Plasticity 3Oguz Umut SALMAN and Roberta BAGGIO1.1. Introduction 31.2. The model 61.2.1. Linear stability analysis 91.3. Numerical implementation 111.4. Simulation results 121.4.1. Stress field of a single-edge dislocation 121.4.2. Dislocation annihilation 131.4.3. Homogeneous nucleation 141.5. Conclusion 181.6. References 18Chapter 2. Effects of Rate, Size, and Prior Deformation in Microcrystal Plasticity 25Stefanos PAPANIKOLAOU and Michail TZIMAS2.1. Introduction 252.2. Model 272.3. Effects of loading rates and protocols in crystal plasticity 292.4. Size effects in microcrystal plasticity 362.5. Unveiling the crystalline prior deformation history using unsupervised machine learning approaches 382.6. Predicting the mechanical response of crystalline materials using supervised machine learning 432.7. Summary 482.8. Acknowledgements 492.9. References 49Chapter 3. Dislocation Dynamics Modeling of the Interaction of Dislocations with Eshelby Inclusions 55Sylvie AUBRY, Sylvain QUEYREAU and Athanasios ARSENLIS3.1. Introduction 553.2. Review of existing approaches 573.2.1. Modeling discrete precipitates with DD simulations 573.2.2. Investigation of precipitation strengthening and some related effects 613.3. Dislocation dynamics modeling of dislocation interactions with Eshelby inclusions 633.3.1. Stress field and forces at dislocation lines 633.3.2. Stress at a point induced by an inclusion 643.3.3. Force on a dislocation coming from an inclusion 643.3.4. Far field interactions induced by an Eshelby inclusion 683.3.5. Parallel implementation 683.4. DD simulations of the interaction with Eshelby inclusions 693.4.1. Eshelby force for a single dislocation and a single inclusion 693.4.2. Simulations of bulk crystal plasticity 703.5. Conclusion and discussion 773.6. Acknowledgments 793.7. Appendix: derivation of the Eshelby force 803.8. References 82Chapter 4. Scale Transition in Finite Element Simulations of Hydrogen–Plasticity Interactions 87Yann CHARLES, Hung Tuan NGUYEN, Kevin ARDON and Monique GASPERINI4.1. Introduction 874.2. Modeling assumptions 924.2.1. Crystal plasticity mechanical behavior 924.2.2. Hydrogen transport equation 934.2.3. Implementation 954.2.4. Mechanical parameters 964.3. Identification of a trap density function at the crystal scale 974.3.1. Geometry, mesh, and boundary conditions applied on the polycrystals 984.3.2. Results 1004.4. Adaptation of the Dadfarnia’s model at the crystal scale 1044.4.1. Formulation at the polycrystal scale 1044.4.2. Application to single crystals 1064.4.3. Boundary and initial conditions 1074.4.4. Crystal orientations 1084.4.5. Results 1084.4.6. Consequences on hydrogen transport through a polycrystalline bar 1134.5. Conclusion 1184.6. Appendix: Numbering of the slip systems in the UMAT 1184.7. References 119Part 2. Mechanics and Physics of Soft Solids 131Chapter 5. Compression of Fiber Networks Modeled as a Phase Transition 133Prashant K. PUROHIT5.1. Introduction 1335.2. Experimental observations in compressed fibrin clots and CNT forests 1345.2.1. Compression of platelet-poor plasma clots and platelet-rich plasma clots 1345.2.2. Compression of CNT forests coated with alumina 1385.3. Theoretical model based on continuum theory of phase transitions 1415.3.1. Compression of PPP and PRP clots 1415.3.2. Phase transition theory 1435.3.3. Effect of liquid pumping 1455.3.4. Application of phase transition model to PPP and PRP clots 1465.3.5. Predictive capability of our model 1485.3.6. Application of phase transition model to CNT networks 1485.4. Conclusion 1515.5. References 153Chapter 6. Mechanics of Random Networks of Nanofibers with Inter-Fiber Adhesion 157Catalin R. PICU and Vineet NEGI6.1. Introduction 1576.2. Mechanics in the presence of adhesion 1606.2.1. The adhesive interaction of two fibers 1606.2.2. Triangle of fiber bundles 1636.3. Structure of non-crosslinked networks with inter-fiber adhesion 1656.4. Tensile behavior of non-crosslinked networks with inter-fiber adhesion 1696.5. Structure of networks with inter-fiber adhesion and crosslinks 1716.6. Tensile behavior of crosslinked networks with inter-fiber adhesion 1736.7. Conclusion 1796.8. References 180Chapter 7. Surface Effects on Elastic Structures 185Hadrien BENSE, Benoit ROMAN and José BICO7.1. Introduction 1857.2. Liquid surface energy 1867.2.1. Can a liquid deform a solid? 1867.2.2. Slender structures 1877.2.3. Wrapping a cylinder 1887.2.4. Capillary origamis 1907.3. Dielectric elastomers: a surface effect? 1927.3.1. Introduction: electrostatic energy of a capacitor as a surface energy 1927.3.2. Mechanics of dielectric elastomers 1947.3.3. Buckling experiments 2027.4. Conclusion 2097.5. References 210Chapter 8. Stress-driven Kirigami: From Planar Shapes to 3D Objects 215Alexandre DANESCU, Philippe REGRENY, Pierre CRÉMILIEU and Jean-Louis LECLERCQ8.1. Introduction 2158.2. Bilayer plates with pre-stress 2168.3. Constant curvature ribbons and geodesic curvature 2198.3.1. Experimental evidence 2208.3.2. Geodesic objects 2228.4. Directional bending of large surfaces 2238.4.1. Photonic crystals tubes 2248.4.2. Control the directional bending 2258.5. Conclusion 2278.6. References 227Chapter 9. Modeling the Mechanics of Amorphous Polymer in the Glass Transition 231Hélène MONTES, Aude BELGUISE, Sabine CANTOURNET and François LEQUEUX9.1. Introduction 2319.2. Modeling the mechanics of amorphous 2339.2.1. Input physics 2339.2.2. Temperature dependence of the intrinsic relaxation times 2359.2.3. Length scales in the model 2369.2.4. Numerical implementation 2379.3. Linear regime in bulk geometry 2399.3.1. Stress relaxation 2399.3.2. Numerical predictions versus experiments in the linear regime 2409.3.3. Role of elastic coupling between domains 2419.4. Linear regime in confined geometries 2449.4.1. Apparent linear viscoelasticity in various geometries 2449.4.2. Comparison of the results of our model with the observation of Tg shift in filled elastomers 2479.4.3. Role of mechanical coupling in confined geometry 2509.4.4. Conclusion on the effects of confinement 2529.5. Nonlinear mechanics 2539.5.1. Input of nonlinearities 2549.5.2. Results of the model 2559.5.3. Role of elastic coupling in the nonlinear regime 2569.6. Conclusion 2579.7. Appendix 2589.8. References 259List of Authors 263Index 267