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The Theory of Composites

The Theory of Composites

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: July 2002
  • availability: Unavailable - out of print
  • format: Hardback
  • isbn: 9780521781251

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  • 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.

    • Very broad overview of rapidly developing subject
    • Mathematically rigorous presentation
    • Comprehensive references
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    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

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    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.

  • Author

    Graeme W. Milton, University of Utah

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