This extended and updated new edition captures developments and results since the original edition and includes a new chapter on two-dimensional thermoelectricity, which concerns itself with effects coupling thermal and electrical conduction in the media.
The book starts with a novel unified approach to homogenization, and develops a general theory of microstructure-independent (exact) relations for composite materials that applies to most physical properties of interest, such as conductivity, elasticity, piezoelectricity, thermoelectricity etc. Its methods allow one to obtain a complete list of exact relations in each physical context of interest.
Key Features:
- Homogenization theory for composite media developed in a novel unified framework covering many physical contexts, such as conductivity, elasticity, piezoelectricity, etc.
- Has complete lists of exact relations and links in all physically relevant contexts
- Can be used by practitioners, who are not mathematicians by consulting Part III of the book written with such an audience in mind
- Would be of interest to broader community of mathematicians in the area of Calculus of Variations
Table of Contents:
Preface
Acknowledgements
Author biography
1 Introduction
Part I Mathematical theory of composite materials
2 Material properties and governing equations
3 Composite materials
Part II General theory of exact relations and links
4 Exact relations
5 Links
6 Computing exact relations and links
Part III Case studies
7 Introduction
8 Conductivity with Hall effect
9 Elasticity
10 Piezoelectricity
11 Thermoelasticity
12 Thermoelectricity
Part IV Appendices
13 Closedness of E( ) B1 and J(B1) for conductivity and elasticity
14 Characterization of all global Jordan isomorphisms
15 Jordan subalgebras of real symmetric matrices
16 A polycrystalline L-relation that is not exact
17 Multiplication of SO(3) irreps in endomorphism algebras
About the Author :
Yury Grabovsky is a professor at the Department of Mathematics at Temple University, where his research interests include the calculus of variations on the mathematics side and continuum mechanics on the physics side. His latest work was on the mathematical theory of composite materials, the buckling of slender bodies, such as plates, rods, and shells, and understanding the stability of equilibrium configurations with phase boundaries in nonlinear elasticity. After graduating with a PhD from the Courant Institute of Mathematical Sciences, New York University, Yury spent a year as a postdoc at the Center for Nonlinear Analysis at Carnegie Mellon University, and three years as a Wylie Instructor at the University of Utah. In 1999 he was hired as a tenure-track Assistant Professor by Temple University. Yury enjoys teaching and performing research with students. His webpage on using continued fractions in the design of calendar systems routinely draws the attention of media every leap year. It has been translated into Portuguese and published in a journal for mathematics schoolteachers Educação e Matemática.
