Local and Nonlocal Micromechanics of Heterogeneous Materials [electronic resource] / by Valeriy A. Buryachenko.

Chapter 1. Introduction -- Chapter 2. Foundations of Solid Mechanics -- Chapter 3. Green’s Functions, Eshelby and Related Tensors -- Chapter 4. Multiscale Analysis of the Multiple Interacting Inclusions Problem: Finite Number of Interacting Inclusions -- Chapter 5. Statistical Description of Composite Materials -- Chapter 6. Effective Properties and Energy Methods in Thermoelasticity and Thermoelectroelasticity of Composites -- Chapter 7. General Integral Equations of Micromechanics of Composite Materials -- Chapter 8. Multiparticle Effective Field and Related Methods in Micromechanics of Random Structure Composites -- Chapter 9. Basic Representations of New background of Micromechanics -- Chapter 10. Inhomogeneity of the First and Second Statistical Moments of Stresses Inside the Heterogeneities of CMs -- Chapter 11. Interface integral technique in thermoelasticity of random structure matrix CMs -- Chapter 12. Nonlinear Problems in Micromechanics of CMs -- Chapter 13. Nonlocal Effects in Micromechanics of Locally Elastic CMs -- Chapter 14. Micromechanics of Strongly Nonlocal Strain-Type and Weakly Nonlocal CMs -- Chapter 15. Subsequent Generalizations of Theory and Related Problems -- Chapter 16. Bond-Based Peridynamics -- Chapter 17. Background of Peridynamic Micromechanics -- Chapter 18. Peridynamic Micromechanics of Random Structure Composites -- Chapter 19. Computational homogenization in linear peridynamic micromechanics of periodic structure CM -- Chapter 20. Conclusion -- Chapter 21. Appendix.

This book presents the micromechanics of random structure heterogeneous materials, a multidisciplinary research area that has experienced a revolutionary renascence at the overlap of various branches of materials science, mechanical engineering, applied mathematics, technical physics, geophysics, and biology. It demonstrates intriguing successes of unified rigorous theoretical methods of applied mathematics and statistical physics in material science of microheterogeneous media. The prediction of the behaviour of heterogeneous materials by the use of properties of constituents and their microstructure is a central problem of micromechanics. This book is the first in micromechanics where a successful effort of systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature is attempted. The uniqueness of the book lies in its development and expressive representation of statistical methods quantitatively describing random structures which are at most adopted for the forthcoming evaluation of a wide variety of macroscopic transport, electromagnetic, strength, and elastoplastic properties of heterogeneous materials. Applies the unified generalized theory to analze the broadest range of problems Sheds light on opportunities for a fundamentally new generalized theory leading to discovery of fundamentally new effects critical for a wide range of nonlinear and nonlocal problems Successfully combines advanced numerical methods for analysis of a finite number of interacting inhomogeneities in either the bounded or unbounded domains .