Micromechanics of Heterogeneous Materials

- Introduction.
- Foundations of Solid Mechanics.
- Green's Function, Eshelby and Related Tensors.
- Multiscale Analysis of Multiple Interacting Inclusions Problem: Finite Number of Interactiong Inclusions.
- Statistical Description of Composite Materials.
- Effective Properties and Effective Energy Functions.
- General Integral Equations of Micromechanics of Composite Materials.
- Energy Methods in Themoelasticity of Composite Materials.
- Multiparticle Effective Field and Related Methods in micromechanics of Random Structure Composites.
- Generalization of the Multiparticle Effective Field Method in Static of Random Structure Matrix Composites.
- Periodic Structures and Perioid Structures with Random Imperfections.
- Nonlocal Effects in Statistically Homogeneous Random Structure Composites.
- Stress Fluctuations in Random Structure Composites.
- Random Structure Matrix Composites in a Half-Space.
- Effective Limiting Surfaces in the Theory of Nonlinear Composites.
- Nonlinear Composites.
- Some Related Problems.
- Multi-scale Mechanics of Nanocomposites.

The book features unified rigorous theoretical methods of applied mathematics and statistical physics in material science of microheterogeneous media. The prediction of the behavior of heterogeneous materials by the use of properties of constituents and their microstructure is a central issue of micromechanics. This book is the first in micromechanics with a useful and effective demonstration of the systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature.

From the reviews:



"A new addition to the mathematical theory of heterogeneous media, this book presents an overview of some standard methods for estimating or bounding overall properties, together with an extensive exposition of the author's multiparticle effective field method (MEFM) ... . There are 18 chapters in over 600 pages with 1240 references ... bringing the reader's attention to the work of Russian authors. The monograph should serve as a useful reference to researchers in science and engineering disciplines concerned with analysis and design of composite materials." (George J. Dvorak, Mathematical Reviews, Issue 2008 g)

"This book deals with a detailed analysis of heterogeneous materials with special emphasis on composite materials that have ever increasing technological applications. References contain 1240 entries. As such it is invaluable for those working in this field. The author employs mainly statistical methods to analyse such materials which becomes more tractable in view of a large mass of statistical data now available due to sophisticated modern experimental techniques. A lot of materials in the book are based on the author's own research works." (Erdogan S. Suhubi, Zentralblatt MATH, Vol. 1133 (11), 2008)