An Introduction to the Mathematical Theory of Dynamic Materials

  • Konstantin A. Lurie

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

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Konstantin A. Lurie
    Pages 1-16
  3. Konstantin A. Lurie
    Pages 17-49
  4. Konstantin A. Lurie
    Pages 109-139
  5. Back Matter
    Pages 163-181

About this book


This book gives a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes. These materials have diverse applications: tunable left-handed dielectrics, optical pumping with high-energy pulse compression, and electromagnetic stealth technology, to name a few. Of special significance is the participation of dynamic materials in almost every optimal material design in dynamics.

The book discusses some general features of dynamic materials as thermodynamically open systems; it gives their adequate tensor description in the context of Maxwell’s theory of moving dielectrics and makes a special emphasis on the theoretical analysis of spatio-temporal material composites (such as laminates and checkerboard structures). Some unusual applications are listed along with the discussion of some typical optimization problems in space-time via dynamic materials.


This book is intended for applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations. It will also be useful for researchers in the field of smart metamaterials and their applications to optimal material design in dynamics.


Mathematica dielectrics dynamics optimization statics variable vibration

Authors and affiliations

  • Konstantin A. Lurie
    • 1
  1. 1.Worcester Polytechnic InstituteWorcester

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