Random Heterogeneous Materials

Rating:
Summary: A modern and comprehensive treatise of material properties
Review: I had the opportunity to use this text while taking Prof. Torquato's material science course at Princeton. The classnotes were a condensed version of the book, while the book describes all the concepts in more details. The book presents a unified treatment of the basic equations of continuum mechanics (flow, elasticity, conduction, diffusion) from a statistical mechanical viewpoint (heavy use of probability models is made), in composite materials (for example, a material with 'spherical inclusions' of a different physical electrical conductivity from the surrounding medium are added) characterized by effective properties (conductivity, permeability, stiffness, trapping constant). The effective properties are calculated from first principles via various correlation functions (Section I describes the probability functions required for dealing with random media; Section II deals with actual calculations of effective properties). To my knowledge, it is the first comprehensive book on the subject; other texts deal with smaller subsections. In some cases, these techniques were previously available only in the specialized literature. I found the many examples provided in the text to be very helpful. I also enjoyed the section on variational principles in the second half of the book; it provides further examples of how variational calculus can be applied to solve relevant problems (in this case, dealing with the optimization of material properties). Most of the theorems are proved and the proofs are short and so shouldn't be much of a burden. The chemist should know this is mostly a book on mathematics, and so does not provide numerical examples with numbers and units (however, all one needs to do is plug in numbers in the formulas), and doesn't present too many actual real-life physical examples you are likely to deal with in the laboratory. Prerequisites are simple: a bit of linear algebra, tensor calculus (but only in orthogonal euclidean spaces), familiarity with basics of probability theory (you should know what a probability density is). Knowledge of statistical mechanics is helpful but not required. There is, of course, a section on hard sphere packing for which the author is well-known for. The chapter on homogenization theory is one of the most accessible I've seen (no knowledge of functional analysis is required-- so it is perfect for the beginner). This book does not have exercises or problems for the reader (it is not for the undergraduate student-- but rather for researchers in the cross-disciplinary fields), and so requires a certain degree of maturity to absorb the material.

Rating:
Summary: Fundamental book discovering new horizons in micromechanics
Review: The micromechanics of random structure heterogeneous materials is 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. The present book is a perfect reflection of this overlapping. It demonstrats intriguing successes of 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 problem of micromechanics. This book is the first one 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 by Torquato consists of the development and expressive representation of statistical methods quantitatively describing random structures (first part of the book) which are at most adopted for the forthcoming evaluation of a wide variety of macroscopic transport, electromagnetic, elastic, and chemical properties of heterogeneous materials (second part of the book). The popular methods in micromechanics that are essentially one particle ones which are invariant with respect to statistical second and higher order quantities examining the association of one particle relative to other particles. The book by Torquato expressively reflects the explosive character of progress of the modern micromechanics caused by the development of image analyses and computer-simulation methods from one side and improved materials processing from the other hand, since processing controls the prescribed microstructure. This progress in micromechanics is based on the methods of allowing for the statistical mechanics of a multi-particle system considering n-point correlation functions and direct multi-particle interaction of inclusions, and the book presents a universally rigorous scheme of both analyses of the microstructures and prediction of macroscopic properties which leaves room for corrections of their individual elements if improved methods are utilized for the analysis of these individual elements.

This book is a landmark in the area of advanced heterogeneous materials and constitutes an excellent balance of depth and clarity of their representation. Every science library and every individual involved in serious research in heterogeneous materials must have this book which will be interesting for both advanced senior scientists and graduate students.