Self-Consistent Methods for Composites

Composite and heterogeneous materials play an important role in modern material engineering and technology. This volume is devoted to the theory of such materials. Static elastic, dielectric, thermo- and electroconductive properties of composite materials reinforced with ellipsoidal homogeneous and multi-layered inclusions, short and long multi-layered fibers, thin hard and soft inclusions, media with cracks and pores are considered. Self-consistent methods are used as the main theoretical tool for the calculation of static and dynamic properties of heterogeneous materials. This book is the first monograph to develop self-consistent methods and apply these to the solution of problems of electromagnetic and elastic wave propagation in matrix composites and polycrystals. Predictions of the methods are compared with experimental data and exact solutions. Explicit equations and efficient numerical algorithms for the calculation of velocities and attenuation coefficients of the mean (coherent) wave fields propagating in composites and polycrystals are presented.§The book helps materials engineers to predict properties of heterogeneous materials and to create new composite materials which physical properties are optimal to the exploitation conditions. The results of the book are useful for scholars who work on the theory of composite and heterogeneous media.This timely text is the first monograph to develop self-consistent methods and apply these to the solution of problems of electromagnetic and elastic wave propagation in matrix composites and polycrystals. Predictions are compared with experimental data and exact solutions. Explicit equations and efficient numerical algorithms for calculating the velocities and attenuation coefficients of the mean (coherent) wave fields propagating in composites and polycrystals are presented.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.