Random Heterogeneous Materials: Conductivity, Percolation, Modeling

Because heterogeneous materials can be designed to exhibit the best characteristics of their individual constituents, they are ideally suited to modern technologies that require materials with an unusual combination of properties. The study presented in the current work is aimed to approach effective electrical conductivity of various random heterogeneous materials. It starts with the description of a type of modern material with specific morphology. Percolation theory and finite element analysis are used in computations and comparison with experimental results is provided. To understand difficulties with classical approaches, next a two-component composite material on a lattice is studied, followed by discoveries in the electrical field properties. Finally, a new algorithm is suggested, which can be used to find effective properties for any arbitrary morphology. Material covered in this book will be of interest to graduate students and researchers who work on the front edge of physics, materials science, engineering and applied mathematics. All necessary derivations and definitions are included to make the book self-contained and approachable.