Composite Materials: Mathematical Theory and Exact Relations

Composite Materials: Mathematical Theory and Exact Relations

by Yury Grabovsky

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Product Details

ISBN-13: 9780750310499
Publisher: IOP Publishing Ltd
Publication date: 01/20/2017
Series: IOP Expanding Physics Series
Pages: 240
Product dimensions: 7.30(w) x 10.41(h) x 0.74(d)

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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