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.
Table of Content
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.
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