An Introduction to Metamaterials and Waves in Composites

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.

Elastodynamics, Acoustics, and Electrodynamics A note about notation Elastodynamics Acoustics Electrodynamics Plane Waves and Interfaces Plane wave solutions Plane wave solutions in elastodynamicsPlane 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 densityFrequency-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 CloakingTransformations Cloaking of electrical conductivity Cloaking for electromagnetism Inertial acoustic cloaking Transformation-based cloaking in elastodynamics Acoustic metafluids and pentamode materials Waves in Periodic MediaPeriodic media and the Bloch condition Elastodynamics in the quasistatic limit Electromagnetic waves in the quasistatic limitBand gap phenomena in periodic composites Waves in Layered MediaWave equations in layered media Piecewise-constant multilayered media Smoothly varying layered media Propagator matrix approach Periodic layered media Quasistatic homogenization of layered media Epilogue References Index

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.