Overview

Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

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9781611977479

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"Graeme W. Milton is a distinguished professor of mathematics at the University of Utah. He has been awarded Sloan and Packard Fellowships, the 2003 SIAM Ralph Kleinman Prize for research bridging the gap between mathematics and applications, the 2007 Society for Engineering Science Prager Medal for contributions to theoretical mechanics, the 2012 Landauer Medal of the ETOPIM Association for seminal contributions to the field of composite material science, and the 2015 International Prize Tullio Levi-Civita for the Mathematical and Mechanical Sciences. He is a fellow of the Society for Industrial and Applied Mathematics. His main interests are in the fields of composite materials, inverse problems, cloaking theory, discrete networks, electromagnetism, and elasticity theory. He has published over 190 papers and written 2 books and edited a third. He, with his collaborators, are best known for: the """"Bergman–Milton"""" bounds on the complex moduli of composites; the Milton zeta and eta parameters that partly govern the electrical and elastic response of microstructures; the CLM (Cherkaev, Lurie, and Milton) theorem giving exact results for the effective elastic moduli of 2d-composites; the general theory of exact relations for composites; pentamode materials that are a sort of anisotropic gel that can guide stress; metamaterials that can reverse the Hall coefficient; the discoveries of anomalous resonance, ghost sources, cloaking due to anomalous resonance, and active exterior cloaking; and the discovery of a new type of wave, called a field pattern, in microstructures where the moduli vary in both time and space."

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