Random Heterogeneous Materials [Hardcover]

Salvatore Torquato (Author)

Book Description

ISBN-10: 0387951679 | ISBN-13: 978-0387951676 | Publication Date: October 19, 2001 | Edition: Corrected

This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

Editorial Reviews

Review

From the reviews:

"This interdisciplinary book is an excellent example of the modern scope of issues of interest to many sciences, namely applied mathematics, physics, chemistry, material science, engineering, geology and biology…This book is to a high degree self-contained…It is the first of its kind to provide a unified rigorous means of characterizing the microstructure and macroscopic properties of the wide class of heterogeneous materials which are distinct in nature. All these circumstances will mean great use of this volume by researchers in different scientific fields, interested in the study of heterogeneous materials, as well as in the preparation of courses for graduate students of corresponding specialties." (Mathematical Reviews)

"Since the author has been at the forefront of this research field, he has deep insight into many of the theoretical developments of the past two decades, and as a result has produced an outstanding book with many insightful comments. In my opinion, every serious researcher and advanced graduate student who is interested in heterogeneous materials should have a copy of this book.” (Journal of Statistical Physics)

"This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry . . . [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc. . . . [This] is a book which is very important and which merits great attention in the mathematical-statistical community.” (D. Stoyan, Metrika, December 2003)

"Random Hetergeneous Materials should become a standard reference for those beginning a study of random hetergeneous media." (Applied Mechanics Reviews)

"The book at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems.  Furthermore, much of the material has not appeared in any previous book on the subject . . . This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquato’s book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field . . . [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquato’s monograph should make an excellent text for self-study or for a graduate course in disordered materials. It will be welcomed by the physical and materials science communities.” (Christian Brosseau, Optics & Photonics News, February 2003)

"This book ... primarily concerns the mathematical analysis of random structures. This work can serve as a foundation for those who wish to design random heterogeneous structures with specified bulk properties. A major contribution of the book is to clearly and rigorously explain the statistical characterization of the microstructure of these materials ... . An extensive reference list is provided. Random Heterogeneous Materials ... should become a standard reference for those beginning a study of random heterogeneous media." (H.W. Haslach Jr., Applied Mechanics Reviews, 55:4, 2002)

"The aim of the book is to give broad information about random heterogeneous materials, particularly based on microstructural and macrostructural properties of the constituent materials. ... The book is well written and might be very useful to researchers working in the area of composite materials and porous media. I, therefore, strongly recommend to personal users and to the institute libraries to keep the book on their shelves." (Hilmi Demiray, Zentralblatt MATH, 988:13, 2002)

"This book contains an incredible amount of (nontrivial) results, many of which were first obtained by the author himself (in collaboration with his Princeton group). ... A large number of exact results, too many to summarize here, as well as upper and lower bounds for the effective properties are provided together with an extensive list of references (30 pages). This book should be useful to anybody interested in the quantitative study of complex materials, whatever their origin." (M. Baus, Physicalia, 38:4, 2002)

From the Back Cover

 

The study of random heterogeneous materials is an exciting and rapidly growing multidisciplinary endeavor. This field demands a unified rigorous means of characterizing the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials that abound in nature and synthetic products. This book is the first of its kind to provide such an approach. Emphasis is placed on foundational theoretical methods that can simultaneously yield results of practical utility.

The first part of the book deals with the quantitive characterization of the microstructure of heterogeneous materials. The second part of the book treats a wide variety of macroscopic transport, electromagnetic, mechanical, and chemical properties of heterogeneous materials and describes how they are linked to the microstructure of model and real materials. Contemporary topics covered include the statistical mechanics of many-partical systems, the canonical n-point correlation function, percolation theory, computer-simulation methods, image analyses and reconstructions of real materials, homogenization theory, exact property predictions, variational bounds, expansion techniques, and cross property relations.

This clear and authoritative volume will be of particular interest to graduate students and researchers in applied mathematics, physics, chemistry, material sciences, engineering, geophysics, and biology. Moreover, the book is self-contained and approachable by nonspecialist.

Salvatore Torquato is a professor in the Department of Chemistry and in the Materials Institute at Princeton University. He also holds affiliated appointments at Princeton University in applied and Computational Mathematics Program and in Chemical Engineering. Among other honors, he was a John Simon Guggenheim Fellow in 1998. He has published over two hundred journal articles across a variety of scientific disciplines.

Product Details

• Hardcover: 728 pages
• Publisher: Springer; Corrected edition (October 19, 2001)
• Language: English
• ISBN-10: 0387951679
• ISBN-13: 978-0387951676
• Product Dimensions: 9.5 x 7.3 x 1.5 inches
• Shipping Weight: 3 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #368,209 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars A modern and comprehensive treatise of material properties, November 12, 2001

By 

LB (New York, NY) - See all my reviews

This review is from: Random Heterogeneous Materials (Hardcover)

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.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Fundamental book discovering new horizons in micromechanics, December 30, 2001

By 

Valeriy Buryachenko (Air Force Research Laboratory, Dayton, OH, USA.) - See all my reviews

This review is from: Random Heterogeneous Materials (Hardcover)

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.