The Theory of Composites
Out of Print
Part of Cambridge Monographs on Applied and Computational Mathematics
- Author: Graeme W. Milton, University of Utah
- Date Published: May 2002
- availability: Unavailable - out of print October 2015
- format: Hardback
- isbn: 9780521781251
Out of Print
Hardback
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The theory of composite materials is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the past four decades has dramatically increased our understanding of the relationship among the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli that govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This book surveys these exciting developments at the frontier of mathematics and presents many new results.
Read more- Very broad overview of rapidly developing subject
- Mathematically rigorous presentation
- Comprehensive references
Reviews & endorsements
"...there existed no book or review paper that would allow a newcomer to get a general knowledge of the state of the art. The book of Graeme Milton fills this gap, and it does the job in a splendid manner that will make it the reference book on composite materials for a long time." Mathematical Reviews
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×Product details
- Date Published: May 2002
- format: Hardback
- isbn: 9780521781251
- length: 748 pages
- dimensions: 255 x 180 x 44 mm
- weight: 1.612kg
- availability: Unavailable - out of print October 2015
Table of Contents
1. Introduction
2. Equations of interest and numerical approaches
3. Duality transformations
4. Translations and equivalent media
5. Microstructure independent exact relations
6. Exact relations for coupled equations
7. Assemblages of inclusions
8. Tricks for exactly solvable microgeometries
9. Laminate materials
10. Approximations and asymptotic formulae
11. Wave propagation in the quasistatic limit
12. Reformulating the problem
13. Variational principles and inequalities
14. Series expansions
15. Correlation functions and series expansions
16. Other perturbation solutions
17. The general theory of exact relations
18. Analytic properties
19. Y-tensors
20. Y-tensors and effective tensors in circuits
21. Bounds on the properties of composites
22. Classical variational principle bounds
23. Hashin-Shtrikman bounds
24. Translation method bounds
25. Choosing translations and finding geometries
26. Bounds incorporating three-point statistics
27. Bounds using the analytic method
28. Fractional linear transformations for bounds
29. The field equation recursion method
30. G-closure properties and extremal composites
31. Bounding and quasiconvexification.
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