An Introduction to the Mathematical Theory of Dynamic Materials

  • Konstantin A.┬áLurie

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

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Konstantin A. Lurie
    Pages 1-31
  3. Konstantin A. Lurie
    Pages 33-69
  4. Konstantin A. Lurie
    Pages 129-194
  5. Konstantin A. Lurie
    Pages 195-260
  6. Back Matter
    Pages 261-277

About this book


Mathematical treatment to properties of dynamic materials, material substances whose properties are variable in space and time are examined in this book. This new edition emphasizes the differences between material optimization techniques in statics and dynamics. Systems with one spatial coordinate and time are used to illustrate essentials of temporal property change in this setting and prompt forthcoming extensions and technical improvements. Since the release of the first edition, a number of new results have created a more complete picture of unusual effects hidden in spatio-temporal material geometry. This renewed look has revealed a conceptually new mechanism of relaxation of material optimization problems in dynamics, which has led to additional resources for optimization previously concealed in the property layouts.

Dynamic materials are studied in this book from the following perspectives: ability to appear in dissimilar implementations, universality as formations that are thermodynamically open, and unusual effects supported by dynamic materials in mechanical and electromagnetic implementations. Special effects accompanying the wave propagation through material geometries in space-time are analyzed by dynamic (spatio-temporal) laminates for screening the extended domains. An extended classification is provided for activated and kinetic dynamic materials, based on the nonstandard exposition of Maxwell-Minkowski electrodynamics of moving bodies. Unique applications as well as fundamental optimization problems are listed within the discussion.

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 Electromagnetic realization dynamic materials spatio-temporal entity mircro/nanoelectromechanical structures Ferroelectric and ferromagnetic materials vibrational mechanics Activated Elastic Bar Floquet theory longitudinal wave Electrodynamics of Moving Dielectrics dielectric laminate spatio-temporal polycrystallic laminate Isotropic Dielectrics Energy transformation Coaxial transmission optimization for wave equation plane waveguide homogenized electromagnetic field

Authors and affiliations

  • Konstantin A.┬áLurie
    • 1
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

Bibliographic information