Heterogeneous Materials.Pt.1
Linear Transport and Optical Properties
(Sprache: Englisch)
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...
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Klappentext zu „Heterogeneous Materials.Pt.1 “
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.
This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive non-linearities as well as threshold non-linearities, such as brittle fracture and dielectric breakdown. A main goal of this book is to compare two fundamental approaches to describing and predicting materials' properties, namely, the continuum mechanics approach, and those based on the discrete models. The latter models include the lattice models and the atomistic approaches. The book provides comprehensive and up to date theoretical and computer simulation analysis of materials' properties. Typical experimental methods for measuring all of these properties are outlined, and comparison is made between the experimental data and the theoretical predictions. Volume I covers linear properties, while Volume II considers non-linear and fracture and breakdown properties, as well as atomistic modeling. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.
Inhaltsverzeichnis zu „Heterogeneous Materials.Pt.1 “
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.
Bibliographische Angaben
- Autor: Muhammad Sahimi
- 2003, 692 Seiten, Masse: 24 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 0387001670
- ISBN-13: 9780387001678
Sprache:
Englisch
Pressezitat
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)
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