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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
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