The Theory of Composites
Part of Cambridge Monographs on Applied and Computational Mathematics
- Author: Graeme W. Milton, University of Utah
- Date Published: July 2002
- availability: Unavailable - out of print
- format: Hardback
- isbn: 9780521781251
Hardback
Looking for an inspection copy?
Please email academicmarketing@cambridge.edu.au to enquire about an inspection copy of this book
-
Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials. Mathematically, it 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 last five decades (and particularly in the last three decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which 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 2002 book surveys these exciting developments at the frontier of mathematics.
Read more- Very broad overview of rapidly developing subject
- Mathematically rigorous presentation
- Comprehensive references
Reviews & endorsements
' … does the job in a splendid manner that will make i the reference book on composite materials for a long time. It is difficult to give a complete account of such an impressive book … I obviously strongly recommend this book, which should soon become the main reference in the field of composite materials.' MathSciNet
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: July 2002
- format: Hardback
- isbn: 9780521781251
- length: 748 pages
- dimensions: 255 x 180 x 44 mm
- weight: 1.612kg
- availability: Unavailable - out of print
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.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×