Material Substructures in Complex Bodies: From Atomic Level to Continuum
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Table of contents
- Contentsv
- Contributorsxi
- Prefacexiii
- Chapter 1. Asymptotic Continuum Models for Plasmas and Disparate Mass Gaseous Binary Mixtures1
- 1.1 Introduction2
- 1.2 The Kinetic Model6
- 1.3 Moment Method and Conservation Laws for Gas Mixtures: Why it Cannot Apply to Plasmas11
- 1.4 The Plasma Fluid Model18
- 1.5 Scaling Hypotheses29
- 1.6 Expansion of the Interspecies Collision Operators34
- 1.7 Moment Method and Conservation Laws for Plasmas40
- 1.8 Computation of the Fluxes and of the Collision Terms49
- 1.9 Conclusion57
- Chapter 2. Microscopic Foundations of the Mechanics of Gases and Granular Materials63
- 2.1 Introduction63
- 2.2 Kinetic Theory of Smooth Spheres65
- 2.3 Collision Dynamics of Rough Spheres69
- 2.4 The Boltzmann–Enskog Equation72
- 2.5 The Macroscopic Balance Equations74
- 2.6 Concluding Remarks76
- Chapter 3. Quantization of Affine Bodies: Theory and Applications in Mechanics of Structured Media80
- 3.1 Introduction80
- 3.2 Classical Preliminaries82
- 3.3 General Ideas of Quantization125
- Chapter 4. Moving Least-Square Basis for Band-Structure Calculations of Natural and Artificial Cryst163
- 4.1 Introduction164
- 4.2 MLS Basis and Periodicity167
- 4.3 Atomic Crystals and Semiconductors174
- 4.4 PhoXonic Crystals183
- 4.5 Strain-Tunable Photonic Bandgap Materials195
- 4.6 Concluding Remarks201
- Chapter 5. Modelling Ziegler–Natta Polymerization in High Pressure Reactors206
- 5.1 Introduction208
- Modelling the Growth of the Agglomerate (Macroscale)212
- 5.2 Governing Equations212
- 5.3 Initial and Boundary Conditions216
- Modelling the Growth of Microspheres217
- 5.4 Kinematics217
- 5.5 The Governing Equations218
- 5.6 Initial and Boundary Conditions222
- 5.7 Analysis of the Equations in the Microscale with Spherical Symmetry224
- 5.8 Consistency of the Boundary Conditions228
- Bridging the Two Scales. The Complete Model232
- 5.9 Determining the Free Terms in the Macroscopic Transport Equations232
- 5.10 The Complete Model232
- 5.11 Not Evolving Natural Configuration234
- 5.12 Conclusions235
- Chapter 6. Pseudofluids238
- 6.1 Preamble238
- 6.2 Material Element239
- 6.3 Basic Fields242
- 6.4 Measures of Deformation and Distorsion245
- 6.5 Strain Rates and Distorsion Rates248
- 6.6 Inertia Measures250
- 6.7 Relations with Thermal Concepts252
- 6.8 Balance Equations255
- 6.9 Boundary Conditions: Sample Flows258
- 6.10 A Lagrangian Approach259
- Chapter 7. A Thermodynamical Framework Incorporating the Effect of the Thermal History on the Solidi262
- 7.1 Introduction263
- 7.2 Kinematics268
- 7.3 Modeling270
- 7.4 Summary and Conclusions281
- Chapter 8. Effects of Stress on Formation and Properties of Semiconductor Nanostructures284
- 8.1 Overview285
- 8.2 Background285
- 8.3 Effects of Stress on the Formation of Semiconductor Nanostructures295
- 8.4 Stress Effects on the Electronic/Optical Properties of Semiconductor Nanostructures303
- 8.5 Conclusions310
- 9. Continua with Spin Structure314
- 9.1 Introduction314
- 9.2 Spatial Representation316
- 9.3 Referential Description: Invariance with Respect to Relabeling323
- 9.4 Covariant Evolution of Interstitial Point Defects and Disclinations327
- Index335
Stringent industrial requirements for sophisticated performance and circumstantial control of microdevices or nanotechnology manufacturing, and other types of machinery at multiple scales, require complex materials. The adjective ‘complex’ indicates that the substructure influences gross mechanical behaviour in a prominent way and interactions due to substructural changes are represented directly. Examples are liquid crystals, quasi-periodic alloys, polymeric bodies, spin glasses, magnetostrictive materials and ferroelectrics, suspensions, in particular liquids with gas bubbles, polarizable fluids, etc.
The mechanical behaviour of complex bodies described in this book gives rise to a wide variety of challenging problems from the macroscopic- to the nano-world. The chapters composing this book explore various aspects of these problems, giving rise to new areas of discussion together with specific solutions.
Contributors are Carlo Cercignani, Gianfranco Capriz, Pierre Degond, Antonio Fasano, Harley T. Johnson, Sukky Jun, Krishna Kannan, Wing Kam Liu, Alberto Mancini, Paolo Maria Mariano, Ingo Müller, Kumbakonan R. Rajagopal, Jan Jerzy Slawianowski.
The book will be a useful tool for researchers and students working on the basic mathematical and physical problems accruing from the mechanics of materials.
* Leading scientific competence of contributors.
* Clear writing style linking solutions and open problems.
* Suggestions for direct technological applications and new research work.
* Mathematical models for nanotechnology devices.
The mechanical behaviour of complex bodies described in this book gives rise to a wide variety of challenging problems from the macroscopic- to the nano-world. The chapters composing this book explore various aspects of these problems, giving rise to new areas of discussion together with specific solutions.
Contributors are Carlo Cercignani, Gianfranco Capriz, Pierre Degond, Antonio Fasano, Harley T. Johnson, Sukky Jun, Krishna Kannan, Wing Kam Liu, Alberto Mancini, Paolo Maria Mariano, Ingo Müller, Kumbakonan R. Rajagopal, Jan Jerzy Slawianowski.
The book will be a useful tool for researchers and students working on the basic mathematical and physical problems accruing from the mechanics of materials.
* Leading scientific competence of contributors.
* Clear writing style linking solutions and open problems.
* Suggestions for direct technological applications and new research work.
* Mathematical models for nanotechnology devices.