The Theory of Composites (Cambridge Monographs on Applied and Computational Mathematics, Vol. 6)

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.