Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Part 1, based on classical mechanics, studies thermoelastic behavior of crystalline and polymeric solids. Part 2, based on quantum mechanics, focuses on interatomic force laws, behavior of solids, and thermally activated processes. 96 figures. 1983 edition.

Table of Contents for Statistical Mechanics of Elasticity

Part 1. Classical Theory
Chapter 1. Thermoelasticity from the Continuum Viewpoint
1.1 Introduction
1.2 Kinematics of Continua
1.3 Mechanics
1.4 Thermodynamics
1.5 Various Thermodynamic Potentials
1.6 Thermoelastic Stress--Strain Relations
1.7 Thermoelastic Relations for Small Changes from Reference State
1.8 Related thermodynamic Functions
1.9 Elastic Constants in Terms of Displacement Gradients
1.10 Isotropic Solids
Appendix Notation of Thurston (1964)
Chapter 2. Concepts of Classical Statistical Mechanics
2.1 Introduction
2.2 Hamiltonian Mechanics
2.3 Use of Statistics in Statistical Mechanics
2.4 Phase Functions and Time Averages
2.5 Phase Space Dynamics of Isolated Systems
2.6 Systems in Weak Interaction
2.7 Canonical Distribution
2.8 Time Averages versus Ensemble Averages
Chapter 3. Corresponding Concepts in Thermodynamics and Statistical Mechanics
3.1 Introduction
3.2 Empirical Temperature
3.3 Quasi-Static Process
3.4 Phase Functions for Generalized Forces
3.5 First Law of Thermodynamics
3.6 Second Law of Thermodynamics
3.7 Use of Mechanical Variables as Controllable Parameters
3.8 Fluctuations
3.9 Partition Function Relations
3.10 Continuum Formulations of Nonuniform Processes
3.11 Equipartition Theorem
3.12 Entropy from the Information Theory Viewpoint
Chapter 4. Crystal Elasticity
4.1 Introduction
4.2 Bravais Lattices
4.3 The Atomistic Concept of Stress in a Perfect Crystal
4.4 Harmonic and Quasi-Harmonic Approximations
4.5 Thermoelastic Stress-Strain Relations Based on the Harmonic Approximation
4.6 Cauchy Relations
4.7 Stress Ensemble
4.8 Linear Chain with Nearest Neighbor Interactions
4.9 Lattice Dynamics and Crystal Elasticity
Chapter 5. Rubber Elasticity, I
5.1 Introduction
5.2 Relative Roles of Internal Energy and Entropy
5.3 Atomic Structure of Long-Chain Molecules and Networks
5.4 One-Dimensional Polymer Model
5.5 Three-Dimensional Polymer Models
5.6 Network Theory of Rubber Elasticity
Chapter 6. Rubber Elasticity, II
6.1 Introduction
6.2 Curvilinear Coordinates
6.3 Geometric Constraints
6.4 An Example
6.5 Curvilinear Coordinates for Stressed Polymer Chains
6.6 Rigid and Flexible Polymer Models
6.7 Use of S = k log p for Stretched Pol
6.8 Strain Ensemble for Short Freely Jointed Chains
6.9 Stress Ensemble for Chain Molecules
6.10 Statistical Mechanics of Phantom Networks
Addendum. Atomic View of Stress in Polymer Systems
Chapter 7. Rate Theory in Solids
7.1 Introduction
7.2 Impurity Atom Diffusion
7.3 A Simple One-Dimensional Rate Theory
7.4 Exact Normalization
7.5 Many Degrees of Freedom
7.6 Transition-State Assumption
7.7 Brownian Motion
7.8 Kramers Rate Formula
Part 2. Quantum Theory
Chapter 8. Basic Concepts of Quantum Mechanics
8.1 Introduction
8.2 Structure of Classical Mechanics
8.3 Structure of Quantum Mechanics
8.4 Consequences of the Fourier Transform Relation between psi subscript x (x) and psi subscript p (p)
8.5 Extension to Three-Dimensional Motion and to N Particles
8.6 Hydrodynamic Analogy to Quantum Mechanics
8.7 Initial-Value Problems
8.8 Aspects of the Measurement Process
8.9 Some Examples of Stationary States
8.10 Tensor Product of Two Spaces
8.11 Electron Spin
8.12 Identical Particles and the Pauli Principle
Chapter 9. Interatomic Interactions
9.1 Introduction
9.2 Hydrogen Molecule
9.3 Adiabatic Approximation
9.4 Hellmann-Feynman Theorem
9.5 Harmonic Elastic Moduli Based on Hellmann--Feynman Theorem
9.6 Categories of Interatomic Force Laws
Chapter 10. Quantum Statistical Effects
10.1 Introduction
10.2 Quantum Statistical Mechanics
10.3 Quantum Statistical Effects in Crystals
10.4 Quantum Statistics for Polymer Models
10.5 Gaussian Wave Packet Dynamics
10.6 Canonical Ensemble in Terms of Coherent States
10.7 Quantum Effects on Rate Processes
References; Index

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