Self-Consistent Methods for Composites

The book is dedicated to the application of self-consistent methods to the solution of static and dynamic problems of the mechanics and physics of composite materials. The effective elastic, electric, dielectric, thermo-conductive and other properties of composite materials reinforced by ellipsoidal, spherical multi-layered inclusions, thin hard and soft inclusions, short fibers and unidirected multi-layered fibers are considered. Explicit formulas and efficient computational algorithms for the calculation of the effective properties of the composites are presented and analyzed. The method of the effective medium and the method of the effective field are developed for the calculation of the phase velocities and attenuation of the mean (coherent) wave fields propagating in the composites. The predictions of the methods are compared with experimental data and exact solutions for the composites with periodical microstructures. The book may be useful for material engineers creating new composite materials and scholars who work on the theory of composite and non-homogeneous media.

The first in the world literature systematic development of self-consistent schemes (the effective medium and effective field methods) and their different versions in application to the problems of the mechanics and physics of heterogeneous materials Contains many concrete results: explicit formulas for the effective properties of composite materials of various micro structures. These formulas will help material engineers to evaluate influence of details of material micro structures on the effective properties, and to create materials with an optimal specter of the properties Presents comparisons of predictions of different self-consistent schemes with experimental results and numerical solutions existing in the literature. Such comparisons show the area of applications of self-consistent methods and the character of possible errors in their predictions The most important part of the book (the second volume) contains applications of self-consistent methods to the problem of wave propagation through composite materials Self-consistent solutions obtained cover long, middle and short wave regions of propagating waves. This makes the book a unique one: such an analysis does not exist in the monographic literature

Inhalt
Self-consistent methods for scalar waves in composites.- Electromagnetic waves in composites and polycrystals.- Axial elastic shear waves in fiber-reinforced composites.- Diffraction of long elastic waves by an isolated inclusion in a homogeneous medium.- Effective wave operator for a medium with random isolated inclusions.- Elastic waves in a medium with spherical inclusions.- Elastic waves in polycrystals.