Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Interdisciplinary Applied Mathematics, 16)

The interdisciplinary subject of random heterogeneous materials has experienced remarkable growth since the publication of the well-known monograph Statistical Con­ tinuum Theories by Beran ( 1968). Many of these advances, especially those concerning the statistical characterization of the microstructure and its effect on the physical prop­ erties of the material, have not been treated fully in any book. One of the intents of the present book is to fill this gap. This book also distinguishes itself in that it provides a unified rigorous framework to characterize the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials found in nature and synthetic products. Emphasis is placed on providing foundational theoretical methods that can simultaneously yield results of practical utility. This book treats a wide breadth of topics, but the choice of subjects naturally reflects my own interests. The sheer enormity of the field has prevented me from covering many important topics. I apologize to those colleagues, known and unknown, who may not find enough of their own work cited in the ensuing pages.

 

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.