The theory of composites
著者
書誌事項
The theory of composites
（Cambridge monographs on applied and computational mathematics, 6）
Cambridge University Press, c2002
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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