Heterogeneous Materials I: Linear Transport and Optical Properties

by Muhammad Sahimi

Overview

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 Effective-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.

Product Details

ISBN-13:	9780387001678
Publisher:	Springer New York
Publication date:	05/15/2003
Series:	Interdisciplinary Applied Mathematics , #22
Edition description:	2003
Pages:	692
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

Characterization and Modelling of the Morphology.- Characterization of Connectivity and Clustering.- Characterization and Modelling of the Morphology.- Linear Transport and Optical Properties.- Effective Conductivity, Dielectric Constant and Optical Properties: The Continuum Approach.- Effective Conductivity and Dielectric Constant: The Discrete Approach.- Frequency-Dependent Properties: The Discrete Approach.- Rigidity and Elastic Properties: The Continuum Approach.- Rigidity and Elastic Properties: The Discrete Approach.- Rigidity and Elastic Properties of Network Glasses, Prolymers, and Composite Solids: the Discrete Approach.

Editorial Reviews

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)

From the Publisher