Front Cover

Computational Analysis of Structured Media

Copyright

Dedication

Contents

Acknowledgment

Preface

Reference

Chapter 1: Introduction

Reference

Chapter 2: Complex Potentials and R-linear problem

1. Complex potentials

2. R-linear problem

3. Metod of functional equations

Reference

Chapter 3: Constructive homogenization

1. Introduction

2. Deterministic and stochastic approaches

3. Series expansions for the local fields and effective tensors. Traditional approach

4. Schwarz’s method

5. Remark on asymptotic methods

Reference

Chapter 4: From Basic Sums to effective conductivity and RVE)

1. Basic Sums

2. Identical circular inclusions.

3. Representative volume element

4. Method of Rayleigh

Reference

Chapter 5: Introduction to the method of self-similar approximants

1. Brief introduction to extrapolation

2. Algebraic renormalization and self-similar bootstrap

3. Extrapolation problem and self-similar approximants

4. Corrected Padè approximants for indeterminate problem

5. Calculation of critical exponents

6. Interpolation with self-similar root approximants

Reference

Chapter 6: Conductivity of regular composite. Square lattice

1. Introduction

2. Critical point, square array

3. Critical Index s

4. Crossover formula for all concentrations

5. Expansion near the threshold

6. Additive ansatz. Critical amplitude and formula for all concentrations

7. Interpolation with high-concentration Padè approximants

8. Comment on contrast parameter

Reference

Chapter 7: Conductivity of regular composite. Hexagonal array

1. Effective conductivity and critical properties of a hexagonal array of superconducting cylinders

2. Series for hexagonal array of superconducting cylinders

3. Critical Point

4. Critical index and amplitude

5. Critical amplitude and formula for all concentrations

6. Interpolation with high-concentration Padè approximants

7. Discussion of the ansatz

8. Square and hexagonal united

9. Dependence on contrast parameter

Reference

Chapter 8: Effective Conductivity of 3D regular composites

1. Modified Dirichlet problem. Finite number of balls

2. 3D periodic problems

3. Triply periodic functions

4. Functional equations on periodic functions

5. Analytical formulae for the effective conductivity. Discussion and overview of the known results.

6. Non-conducting inclusions embedded in an conducting matrix. FCC lattice

7. Non-conducting inclusions embedded in an conducting matrix. SC and BCC lattices

Reference

Chapter 9: Random 2D composites

1. Critical properties of an ideally conducting composite materials

2. Random composite: stirred or shaken?

3. 2D Conductivity. Dependence on contrast parameter

Reference

Chapter 10: Elastic problem

1. Introduction

2. Method of functional equations for local fields

3. Averaged fields in finite composites

4. Roadmap to composites represented by RVE

5. Effective constants

Reference

Table 11.1: Table of the main analytical formulae. A crosssection is displayed for fibrous composites

Index

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