Composite Materials: Mathematical theory and exact relations
The mathematical method of composites has reached a very high level of maturity and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour.

This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more.
1125757415
Composite Materials: Mathematical theory and exact relations
The mathematical method of composites has reached a very high level of maturity and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour.

This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more.
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Composite Materials: Mathematical theory and exact relations

Composite Materials: Mathematical theory and exact relations

by Privateer
Composite Materials: Mathematical theory and exact relations

Composite Materials: Mathematical theory and exact relations

by Privateer

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Overview

The mathematical method of composites has reached a very high level of maturity and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour.

This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more.

Product Details

ISBN-13: 9780750310482
Publisher: Taylor & Francis
Publication date: 12/12/2016
Series: Code of Federal Regulations, Title 18 Conservation of Power
Sold by: Barnes & Noble
Format: eBook
Pages: 500
File size: 934 KB

About the Author

Yury Grabovsky is an associate professor in the Department of Mathematics in the College of Science and Technology at Temple University, Philadelphia, USA.

Table of Contents

I Mathematical theory of composite materials
1 Material properties and governing equations
2 Mathematical definition of a composite
3 H-limits and G-closures
4 G-closed sets and -quasiconvexity
5 Lamination closure and -convexity

II Exact relations and links
6 Exact relations
7 Links
8 Exact relations with volume fraction information
9 Computing exact relations and links
10 Polycrystalline exact relations

III Case studies
11 2D conductivity with Hall effect
12 3D conductivity with Hall effect
13 Fiber-reinforced conducting composites with Hall effect
14 2D thermoelectricity
15 3D thermoelectricity
16 2D elasticity
17 3D elasticity
18 Fiber-reinforced elastic composites
19 2D Piezoelectricity
20 3D Piezoelectricity
21 Arbitrary number of coupled electric fields

Appendices
A Jordan multialgebras
B Ideals and factor-algebras
C Characterization of all subalgebras of Sym(Rn)
D Lamination exact relations that are not closed under homogenization

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