Heterogeneous Materials I

1. Front Matter

   Pages i-xix

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2. Introduction

   1. Introduction

      Pages 1-14

3. Characterization and Modelling of the Morphology

   1. Front Matter

      Pages 15-15

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   2. Characterization of Connectivity and Clustering

      Pages 16-60

   3. Characterization and Modelling of the Morphology

      Pages 61-107

4. Linear Transport and Optical Properties

   1. Front Matter

      Pages 108-108

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   2. Effective Conductivity, Dielectric Constant and Optical Properties: The Continuum Approach

      Pages 109-208

   3. Effective Conductivity and Dielectric Constant: The Discrete Approach

      Pages 209-310

   4. Frequency-Dependent Properties: The Discrete Approach

      Pages 311-434

   5. Rigidity and Elastic Properties: The Continuum Approach

      Pages 435-560

   6. Rigidity and Elastic Properties: The Discrete Approach

      Pages 561-622

   7. Rigidity and Elastic Properties of Network Glasses, Prolymers, and Composite Solids: the Discrete Approach

      Pages 623-680

5. Back Matter

   Pages 681-770

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8. Rigidity and Elastic Properties: The Discrete Approach 8. 0 Introduction 8. 1 Elastic Networks in Biological Materials 8. 2 Number of Elastic Moduli of a Lattice 8. 3 Numerical Simulation and Finite-Size Scaling 8. 4 Derivation of Elastic Networks from Continuum Elasticity 8. 4. 1 The Born model 8. 4. 2 Shortcomings of the Born model 8. 5 The Central-Force Network 8. 6 Rigidity Percolation 8. 6. 1 Static and dynamic rigidity and ?oppiness of networks 8. 6. 2 The correlation length of rigidity percolation 8. 6. 3 The force distribution 8. 6. 4 Determination of the percolation threshold 8. 6. 4. 1 Moments of the force distribution 8. 6. 4. 2 The pebble game 8. 6. 4. 3 Constraint-counting method 8. 6. 5 Mapping between rigidity percolation and resistor networks 8. 6. 6 Nature of phase transition in rigidity percolation 8. 6. 7 Scaling properties of the elastic moduli 8. 7 Green Function Formulation and Perturbation Expansion 8. 7. 1 E?ective-medium approximation 8. 7. 2 The Born model 8. 7. 3 Rigidity percolation 8. 8 The Critical Path Method 8. 9 Central-Force Networks at Non-zero Temperature and under Stress 8. 10 Shortcomings of the Central-Force Networks 8. 11 Elastic Percolation Networks with Bond-Bending Forces 8. 11. 1 The Kirkwood-Keating model xiv 8. 11. 2 The bond-bending model 8. 11. 3 The percolation thresholds 8. 11. 4 The force distribution 8. 11. 5 Comparison of the central-force and bond-bending networks 8. 11.

• composite
• continuum mechanics
• heterogeneous materials
• materials properties
• mechanics
• modeling
• polymer
• polymers
• simulation

From the reviews:

"This work represents the first part of an impressive two-volume book that describes various theoretical and computational approaches related to effective macroscopic properties of heterogeneous materials. … A main goal is to compare two fundamental directions used to study the heterogeneous materials properties, namely the continuum mechanics approach and the discrete model approach. … This multidisciplinary book is recommended to materials scientists, chemical and mechanical engineers, and applied physicists and mathematicians." (Olivian Simionescu, Zentralblatt MATH, Vol. 1028, 2004)

• Department of Chemical Engineering, University of Southern California, Los Angeles, USA

  Muhammad Sahimi

• Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan, Iran

  Muhammad Sahimi

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