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An Introduction to the Mathematical Theory of Dynamic Materials

  • Book
  • © 2007

Overview

Authors:
  1. Konstantin A. Lurie

    1. Worcester Polytechnic Institute, Worcester

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  • Novel exposition of new mathematical theory developed by the author

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 15)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. A General Concept of Dynamic Materials

    • Konstantin A. Lurie
    Pages 1-16

  3. An Activated Elastic Bar: Effective Properties

    • Konstantin A. Lurie
    Pages 17-49

  4. Dynamic Materials in Electrodynamics of Moving Dielectrics

    • Konstantin A. Lurie
    Pages 51-89

  5. G-closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation

    • Konstantin A. Lurie
    Pages 91-107

  6. Rectangular Microstructures in Space-Time

    • Konstantin A. Lurie
    Pages 109-139

  7. Some Applications of Dynamic Materials in Electrical Engineering and Optimal Design

    • Konstantin A. Lurie
    Pages 141-161

  8. Back Matter

    Pages 163-181
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Keywords

About this book

This book has emerged from the study of a new concept in material science that has been realized about a decade ago. Before that, I had been working for more than 20 years on conventional composites assembled in space and therefore adjusted to optimal material design in statics. The reason for that adjustmentisthatsuchcompositesappearedtobecomenecessaryparticipants in almost any optimal material design related to a state of equilibrium. A theoretical study of conventional composites has been very extensive over a long period of time. It received stimulation through many engineering applications, and some of the results have become a part of modern industrial technology. But again, the ordinary composites are all about statics, or, at the utmost, are related to control over the free vibration modes, a situation conceptually close to a static equilibrium. The world of dynamics appears to be quite di?erent in this aspect. When it comes to motion, the immovable material formations distributed in space alone become insu?cient as the elements of design because they are incapable of getting fully adjusted to the temporal variation in the environment. To be able to adequately handle dynamics, especially the wave motion, the material medium must itself be time dependent, i.e. its material properties should vary in space and time alike. Any substance demonstrating such variation has been termed a dynamic material [1].

Reviews

This book is the first monograph presenting an explicit account of a new material concept:  it introduces and explores formations with parameters variable in both space and time and therefore called dynamic materials (DM). Being thermodynamically open systems, DM may be adjusted to a dynamic environment due to unusual effects produced by their mass/momentum/energy exchange with the environment. A number of such effects forms a basis for technical devices that support energy accumulation and its storage in traveling waves, effective sensing, isolation of extended domains in space-time from the invasion of dynamic disturbances, etc. The DM concept is at the same time theoretically significant as the means of material optimization and design in dynamics based on the ideas conceptually different from those traditionally applicable in statics, such as homogenization. All in all, the book by Lurie represents a fundamental work that will become a source of novel conceptual ideas and engineering applications. (Iliya I. Blekhman,  Materials Physics and Mechanics 11 (2011), pp. 190-193)

Authors and Affiliations

  • Worcester Polytechnic Institute, Worcester

    Konstantin A. Lurie

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