Motivation and overview PART I Microstructural characterization Microstructural descriptors Statistical mechanics of particle systems Unified approach Monodisperse spheres Polydisperse spheres Anisotropic media Cell and random-field models Percolation and clustering Some continuum percolation results Local volume fraction fluctuation computer simulation and image analysis PART II Microstructure property connections Local and homogenized equations Variational Principles Phase-interchange relations Exact results Single-inclusion solutions Effective medium approximations Cluster expansions Exact contrast expansions Rigorous bounds Evaluation of bounds Cross-property relations Appendix A Equilibrium Hard disk program Appendix B Interrelations among 2-3D moduli References Index
Motivation and overview * PART I Microstructural characterization * Microstructural descriptors * Statistical mechanics of particle systems * Unified approach * Monodisperse spheres * Polydisperse spheres * Anisotropic media * Cell and random-field models * Percolation and clustering * Some continuum percolation results * Local volume fraction fluctuation * computer simulation and image analysis * PART II Microstructure property connections * Local and homogenized equations * Variational Principles * Phase-interchange relations * Exact results * Single-inclusion solutions * Effective medium approximations * Cluster expansions * Exact contrast expansions * Rigorous bounds * Evaluation of bounds * Cross-property relations * Appendix A Equilibrium Hard disk program * Appendix B Interrelations among 2-3D moduli* References * Index
This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.
A heterogeneous material consists of domains of different materials or the same material in different states. This book provides graduate students and researchers in applied mathematics, physics, chemistry, materials science and engineering with a unified approach of treating the microstructure and effective properties of heterogeneous media. Although it covers the latest advances in the field, it is written in an accessible style and will be sufficiently well-contained for the non-expert wishing to learn the field.