An Introduction to Metamaterials and Waves in Composites

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ISBN 9781439841570
Cat# K11934



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  • Covers elastodynamic, acoustic, and electrodynamic metamaterials, including negative permittivity materials, artificial magnetic metamaterials, Willis materials in elastodynamics, material based on a Milton-Willis model, and extremal materials
  • Places special emphasis on elastic media and acoustics
  • Explains the Willis equations and their consequences
  • Provides detailed derivations, making the text relatively self-contained
  • Requires no higher level knowledge of wave propagation
  • Includes many illustrations, end-of-chapter problems, and extensive references

Forthcoming solutions manual available upon qualifying course adoption


Requiring no advanced knowledge of wave propagation, An Introduction to Metamaterials and Waves in Composites focuses on theoretical aspects of metamaterials, periodic composites, and layered composites. The book gives novices a platform from which they can start exploring the subject in more detail.

After introducing concepts related to elasticity, acoustics, and electrodynamics in media, the text presents plane wave solutions to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the plane wave expansion of sources as well as scattering from curved interfaces, specifically spheres and cylinders. The author then covers electrodynamic, acoustic, and elastodynamic metamaterials. He also describes examples of transformations, aspects of acoustic cloaking, and applications of pentamode materials to acoustic cloaking. With a focus on periodic composites, the text uses the Bloch-Floquet theorem to find the effective behavior of composites in the quasistatic limit, presents the quasistatic equations of elastodynamic and electromagnetic waves, and investigates Brillouin zones and band gaps in periodic structures. The final chapter discusses wave propagation in smoothly varying layered media, anisotropic density of a periodic layered medium, and quasistatic homogenization of laminates.

This book provides a launch pad for research into elastic and acoustic metamaterials. Many of the ideas presented have yet to be realized experimentally—the book encourages readers to explore these ideas and bring them to technological maturity.

Table of Contents

Elastodynamics, Acoustics, and Electrodynamics
A note about notation

Plane Waves and Interfaces
Plane wave solutions
Plane wave solutions in elastodynamics
Plane wave solutions in acoustics
Plane wave solutions in electrodynamics
Wave propagation through a slab

Sources and Scattering
Plane wave expansion of sources
Single scattering from spheres
Multiple scattering

Electrodynamic Metamaterials
A model for the permittivity of a medium
Negative permittivity materials
Artificial magnetic metamaterials
Negative refraction and perfect lenses

Acoustic and Elastodynamic Metamaterials
Dynamic mass density
Frequency-dependent moment of inertia
Negative elastic moduli
Band gaps, negative index and lenses
Anisotropic density
Willis materials in elastodynamics
A Milton-Willis model material
Extremal materials

Transformation-Based Methods and Cloaking
Cloaking of electrical conductivity
Cloaking for electromagnetism
Inertial acoustic cloaking
Transformation-based cloaking in elastodynamics
Acoustic metafluids and pentamode materials

Waves in Periodic Media
Periodic media and the Bloch condition
Elastodynamics in the quasistatic limit
Electromagnetic waves in the quasistatic limit
Band gap phenomena in periodic composites

Waves in Layered Media
Wave equations in layered media
Piecewise-constant multilayered media
Smoothly varying layered media
Propagator matrix approach
Periodic layered media
Quasistatic homogenization of layered media




Author Bio(s)

Biswajit Banerjee works at Industrial Research Limited in Auckland, New Zealand, where he researches and develops elastic wave control and deformation sensing technologies. He was previously a research professor of mechanical engineering and mathematics at the University of Utah.

Editorial Reviews

… this book provides a thorough and modern introduction to a rapidly developing field of research with enormous potential for application.
—Chris Linton, Contemporary Physics, March 2012