Heterogeneous Materials

1. Front Matter

   Pages i-xx

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2. Introduction Volume II

   1. Introduction Volume II

      Pages 1-4

3. Characterization of Surface Morphology

   1. Characterization of Surface Morphology

      Pages 5-22

4. Effective Properties of Heterogeneous Materials with Constitutive Nonlinearities

   1. Front Matter

      Pages 24-24

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   2. Nonlinear Conductivity and Dielectric Constant: The Continuum Approach

      Pages 25-61

   3. Nonlinear Conductivity, Dielectric Constant, and Optical Properties: The Discrete Approach

      Pages 62-161

   4. Nonlinear Rigidity and Elastic Moduli: The Continuum Approach

      Pages 162-203

5. Fracture and Breakdown of Heterogeneous Materials

   1. Front Matter

      Pages 206-206

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   2. Electrical and Dielectric Breakdown: The Discrete Approach

      Pages 207-246

   3. Fracture: Basic Concepts and Experimental Techniques

      Pages 247-289

   4. Brittle Fracture: The Continuum Approach

      Pages 290-364

   5. Brittle Fracture: The Discrete Approach

      Pages 365-451

6. Atomistic and Multiscale Modeling of Materials

   1. Front Matter

      Pages 454-454

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   2. Atomistic Modeling of Materials

      Pages 455-548

   3. Multiscale Modeling of Materials: Joining Atomistic Models with Continuum Mechanics

      Pages 551-589

7. Back Matter

   Pages 591-637

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Disorder plays a fundamental role in many natural and man-made systems that are of industrial and scienti?c importance. Of all the disordered systems, hete- geneous materials are perhaps the most heavily utilized in all aspects of our daily lives, and hence have been studied for a long time. With the advent of new - perimental techniques, it is now possible to study the morphology of disordered materials and gain a much deeper understanding of their properties. Novel te- niqueshavealsoallowedustodesignmaterialsofmorphologieswiththeproperties that are suitable for intended applications. With the development of a class of powerful theoretical methods, we now have the ability for interpreting the experimental data and predicting many properties of disordered materials at many length scales. Included in this class are ren- malization group theory, various versions of effective-medium approximation, percolation theory, variational principles that lead to rigorous bounds to the - fective properties, and Green function formulations and perturbation expansions. Thetheoreticaldevelopmentshavebeenaccompaniedbyatremendousincreasein the computational power and the emergence of massively parallel computational strategies. Hence, we are now able to model many materials at molecular scales and predict many of their properties based on ?rst-principle computations.

• computer simulation
• continuum mechanics
• fracture
• materials properties
• mechanics
• modeling
• simulation

From the reviews:

"There has been increasing interest in recent years in the synthesis and study of materials structured on the nanoscale and mesoscale. This two-volume treatment by Muhammad Sahimi of complex, disordered materials is thus particularly timely. … The second volume also pays significant attention to fracture in heterogeneous materials. … It is likely that this material will be of greatest interest to scientists in physics, engineering, chemistry, and materials science. … well written in an accessible and readable style with detailed descriptions of the models … ." (Ward H. Thompson, MRS Bulletin, Vol. 30, February, 2005)

"The book is divided into two volumes. … Volume II contains an extensive collection of nonlinear models, including models of fracture and breakdown and atomistic models. … is well organized, contains necessary details and explanations and discusses predictions of the models … . a useful contribution to the literature devoted to inhomogeneous materials. It can be recommended to a wide range of readers: from actively working investigators in the field … to engineering students (as additional reading related to material science courses)." (Alexander G. Kolpakov, Mathematical Reviews, 2004e)

"The second volume of this multidisciplinary book deals with the study of transport processes in nonlinear heterogeneous materials. One derives effective properties of disordered materials providing constitutive nonlinearities … . This multidisciplinary book is recommended to materials scientists, chemical and mechanical engineers, and applied physicists and mathematicians." (Olivian Simionescu, Zentralblatt MATH, Vol. 1028, 2004)

"The second volume of Sahimi’s magnum opus deals with nonlinearities in the behavior of heterogenous materials. … Apart from basic concepts and experimental techniques, the continuum and discrete approaches to fracture are considered in great detail. …Sahimi’s two books … present an exhaustive account of the developments in heterogeneous materials research. They are outstanding contributions in the field." (Eva Gregorova, Materials World, Vol. 13 (12), 2005)

"There has been increasing interest … in the synthesis and study of materials structured on the nanoscale and mesoscale. This two-volume treatment by Muhammad Sahimi of complex, disordered materials is thus particularly timely. … this material will be of greatest interest to scientists in physics, engineering, chemistry, and materials science. The books are well written in an accessible and readable style with detailed descriptions of the models and derivations of the theoretical approaches. … useful for graduate students and researchers beginning in the field … ." (Ward H. Thompson, MRS Bulletin, Vol. 30, February, 2005)

"This book covers several major properties of heterogeneous materials … . The book will be quite useful for engineers working on composite materials; it will allow them to look into not only the optical properties of these materials, but also their mechanical and thermal characteristics." (Hiroshi Mataki, Optics & Photonics News, Vol. 16 (10), 2005)

• Department of Chemical Engineering, University of Southern California, Los Angeles, USA

  Muhammad Sahimi

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