Foundations of Solid Mechanics.- Green's Functions, Eshelby and Related Tensors.- Multiscale Analysis of the Multiple Interacting Inclusions Problem: Finite Number of Interacting Inc.- Statistical Description of Composite Materials.- Effective Properties and Energy Methods in Thermoelasticity of Composite Materials.- General Integral Equations of Micromechanics of Composite Materials.- Multiparticle Effective Field and Related Methods in Micromechanics of Random Structure Composites.- Some Related Methods in Micromechanics of Random Structure Composites.- Generalization of the MEFM in Random Structure Matrix Composites.- Periodic Structures and Periodic Structures with Random Imperfections.- Nonlocal Effects in Statistically Homogeneous and Inhomogeneous 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.- Multiscale Mechanics of Nanocomposites.- Conclusion. Critical Analysis of Some Basic Concepts of Micromechanics.
Here is an accurate and timely account of micromechanics, which spans materials science, mechanical engineering, applied mathematics, technical physics, geophysics, and biology. The book features rigorous and unified theoretical methods of applied mathematics and statistical physics in the material science of microheterogeneous media. Uniquely, it offers a useful demonstration of the systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature.
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.