Electromagnetic Properties of Multiphase Dielectrics - A Primer on Modeling, Theory and Computation

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with
tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The ``tailored'' aggregate properties are
achieved by combining an easily moldable base matrix with particles
having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in ``hot spots.'' This necessitates
a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.
A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:
(1) The foundations of Maxwell's equations,
(2) Basic homogenization theory,
(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),
(4) Numerical methods and
(5) An introduction to select biological problems.
The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

List of contents

Multiphase continua, an introduction.- Elementary notation and mathematical operations.- Governing electromagnetics: Maxwell's equations.- Classical linear constitutive behavior.- Extraction of macroscopic effective properties.- Coupled effects: Joule-heating.- Some basic principles of continuum mechanics.- Basic time-stepping schemes.- A model problem: dielectrics undergoing multifield processes.- Concluding remarks and emerging applications in the biological sciences.

About the author

AUTHOR BIOGRAPHY: T. I. Zohdi is currently Professor and Vice Chair for Instruction in the Department of Mechanical Engineering and Chair of the Engineering Science Program at UC Berkeley.

He  received his  Ph.D. in 1997 in Computational and Applied Mathematics from UT Austin and his Habilitation in Mechanics from the Leibniz Universitaet in  Hannover, Germany in 2002.

His main research interests are in micromechanical material design, particulate flow and  the mechanics  of  high-strength fabric, with and emphasis on computational approaches for  nonconvex multiscale-multiphysics inverse problems, particularly addressing the crucial issue of how large numbers of microconstituents interact to produce macroscale aggregate behavior. He published over 85 archival refereed journal papers and four books.

In 2000,  he  received the Zienkiewicz Prize and the Medal, and in 2003,he received the Junior Achievement Award for the American Academy of Mechanics. He is a Fellow of the United States Association for Computational Mechanics (USACM) and the International Association for Computational Mechanics (IACM), and is  currently  Vice President of USACM, and will become the USACM President in 2012.

Summary

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with 
tailored  electromagnetic  (dielectric) properties are necessary for a successful  overall design.  The ``tailored'' aggregate properties are
achieved by combining an easily moldable  base matrix with particles
 having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response,  which can be important to determine possible failures in ``hot spots.'' This necessitates 
 a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.  
A central  objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:
(1) The foundations of  Maxwell's equations,
(2) Basic homogenization theory,
(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),
(4) Numerical methods and
(5) An introduction to select biological problems.
The text can be viewed as a research monograph  suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Additional text

From the book reviews:
“In this succinct monograph, the author provides readers with a clear idea of how to derive and numerically solve coupled systems involving electromagnetic, thermal, mechanical and chemical processes. The book consists of 10 chapters. … this book is well written and should be interesting to a wide spectrum of researchers and students in the physical sciences, engineering and applied mathematics.” (JiChun Li, Mathematical Reviews, August, 2014)

Report

From the book reviews:
"In this succinct monograph, the author provides readers with a clear idea of how to derive and numerically solve coupled systems involving electromagnetic, thermal, mechanical and chemical processes. The book consists of 10 chapters. ... this book is well written and should be interesting to a wide spectrum of researchers and students in the physical sciences, engineering and applied mathematics." (JiChun Li, Mathematical Reviews, August, 2014)

Product details

• Authors: Tarek I Zohdi, Tarek I. Zohdi
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 07.05.2014
• EAN: 9783642426612
• ISBN: 978-3-642-42661-2
• No. of pages: 178
• Dimensions: 155 mm x 10 mm x 235 mm
• Weight: 306 g
• Illustrations: XVIII, 178 p.
• Series: Lecture Notes in Applied and Computational Mechanics; Lecture Notes in Applied and Computational Mechanics
• Subjects: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering; B, engineering, Civil Engineering, Solid Mechanics, Theoretical and Applied Mechanics, Mechanics, Mechanics of solids, Mechanics, Applied, Electromagnetic Properties;Multiphase Dielectrics