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

Chapter 1: Homogeneous Dislocation Nucleation in Landau Theory of Crystal Plasticity

• • 1.1. Introduction
• • 1.2. The model
• • 1.2.1. Linear stability analysis
• • 1.3. Numerical implementation
• • 1.4. Simulation results
• • 1.4.1. Stress field of a single-edge dislocation
• • 1.4.2. Dislocation annihilation
• • 1.4.3. Homogeneous nucleation
• • 1.5. Conclusion
• • 1.6. References

Chapter 2: Effects of Rate, Size, and Prior Deformation in Microcrystal Plasticity

• • 2.1. Introduction
• • 2.2. Model
• • 2.3. Effects of loading rates and protocols in crystal plasticity
• • 2.4. Size effects in microcrystal plasticity
• • 2.5. Unveiling the crystalline prior deformation history using unsupervised machine learning approaches
• • 2.6. Predicting the mechanical response of crystalline materials using supervised machine learning
• • 2.7. Summary
• • 2.8. Acknowledgements
• • 2.9. References

Chapter 3: Dislocation Dynamics Modeling of the Interaction of Dislocations with Eshelby Inclusions

• • 3.1. Introduction
• • 3.2. Review of existing approaches
• • 3.2.1. Modeling discrete precipitates with DD simulations
• • 3.2.2. Investigation of precipitation strengthening and some related effects
• • 3.3. Dislocation dynamics modeling of dislocation interactions with Eshelby inclusions
• • 3.3.1. Stress field and forces at dislocation lines
• • 3.3.2. Stress at a point induced by an inclusion
• • 3.3.3. Force on a dislocation coming from an inclusion
• • 3.3.4. Far field interactions induced by an Eshelby inclusion
• • 3.3.5. Parallel implementation
• • 3.4. DD simulations of the interaction with Eshelby inclusions
• • 3.4.1. Eshelby force for a single dislocation and a single inclusion
• • 3.4.2. Simulations of bulk crystal plasticity
• • 3.5. Conclusion and discussion
• • 3.6. Acknowledgments
• • 3.7. Appendix: derivation of the Eshelby force
• • 3.8. References

Chapter 4: Scale Transition in Finite Element Simulations of Hydrogen–Plasticity Interactions

• • 4.1. Introduction
• • 4.2. Modeling assumptions
• • 4.2.1. Crystal plasticity mechanical behavior
• • 4.2.2. Hydrogen transport equation
• • 4.2.3. Implementation
• • 4.2.4. Mechanical parameters
• • 4.3. Identification of a trap density function at the crystal scale
• • 4.3.1. Geometry, mesh, and boundary conditions applied on the polycrystals
• • 4.3.2. Results
• • 4.4. Adaptation of the Dadfarnia’s model at the crystal scale
• • 4.4.1. Formulation at the polycrystal scale
• • 4.4.2. Application to single crystals
• • 4.4.3. Boundary and initial conditions
• • 4.4.4. Crystal orientations
• • 4.4.5. Results
• • 4.4.6. Consequences on hydrogen transport through a polycrystalline bar
• • 4.5. Conclusion
• • 4.6. Appendix: Numbering of the slip systems in the UMAT
• • 4.7. References

Chapter 5: Compression of Fiber Networks Modeled as a Phase Transition

• • 5.1. Introduction
• • 5.2. Experimental observations in compressed fibrin clots and CNT forests
• • 5.2.1. Compression of platelet-poor plasma clots and platelet-rich plasma clots
• • 5.2.2. Compression of CNT forests coated with alumina
• • 5.3. Theoretical model based on continuum theory of phase transitions
• • 5.3.1. Compression of PPP and PRP clots
• • 5.3.2. Phase transition theory
• • 5.3.3. Effect of liquid pumping
• • 5.3.4. Application of phase transition model to PPP and PRP clots
• • 5.3.5. Predictive capability of our model
• • 5.3.6. Application of phase transition model to CNT networks
• • 5.4. Conclusion
• • 5.5. References

Chapter 6: Mechanics of Random Networks of Nanofibers with Inter-Fiber Adhesion

• • 6.1. Introduction
• • 6.2. Mechanics in the presence of adhesion
• • 6.2.1. The adhesive interaction of two fibers
• • 6.2.2. Triangle of fiber bundles
• • 6.3. Structure of non-crosslinked networks with inter-fiber adhesion
• • 6.4. Tensile behavior of non-crosslinked networks with inter-fiber adhesion
• • 6.5. Structure of networks with inter-fiber adhesion and crosslinks
• • 6.6. Tensile behavior of crosslinked networks with inter-fiber adhesion
• • 6.7. Conclusion
• • 6.8. References

Chapter 7: Surface Effects on Elastic Structures

• • 7.1. Introduction
• • 7.2. Liquid surface energy
• • 7.2.1. Can a liquid deform a solid?
• • 7.2.2. Slender structures
• • 7.2.3. Wrapping a cylinder
• • 7.2.4. Capillary origamis
• • 7.3. Dielectric elastomers: a surface effect?
• • 7.3.1. Introduction: electrostatic energy of a capacitor as a surface energy
• • 7.3.2. Mechanics of dielectric elastomers
• • 7.3.3. Buckling experiments
• • 7.4. Conclusion
• • 7.5. References

Chapter 8: Stress-driven Kirigami: From Planar Shapes to 3D Objects

• • 8.1. Introduction
• • 8.2. Bilayer plates with pre-stress
• • 8.3. Constant curvature ribbons and geodesic curvature
• • 8.3.1. Experimental evidence
• • 8.3.2. Geodesic objects
• • 8.4. Directional bending of large surfaces
• • 8.4.1. Photonic crystals tubes
• • 8.4.2. Control the directional bending
• • 8.5. Conclusion
• • 8.6. References

Chapter 9: Modeling the Mechanics of Amorphous Polymer in the Glass Transition

• • 9.1. Introduction
• • 9.2. Modeling the mechanics of amorphous
• • 9.2.1. Input physics
• • 9.2.2. Temperature dependence of the intrinsic relaxation times
• • 9.2.3. Length scales in the model
• • 9.2.4. Numerical implementation
• • 9.3. Linear regime in bulk geometry
• • 9.3.1. Stress relaxation
• • 9.3.2. Numerical predictions versus experiments in the linear regime
• • 9.3.3. Role of elastic coupling between domains
• • 9.4. Linear regime in confined geometries
• • 9.4.1. Apparent linear viscoelasticity in various geometries
• • 9.4.2. Comparison of the results of our model with the observation of Tg shift in filled elastomers
• • 9.4.3. Role of mechanical coupling in confined geometry
• • 9.4.4. Conclusion on the effects of confinement
• • 9.5. Nonlinear mechanics
• • 9.5.1. Input of nonlinearities
• • 9.5.2. Results of the model
• • 9.5.3. Role of elastic coupling in the nonlinear regime
• • 9.6. Conclusion
• • 9.7. Appendix
• • 9.8. References