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The Theory of Composites
Duality transformations in two-dimensional media
monograph
Author(s):
Graeme W. Milton
Publication date
(Online):
2009
Publisher:
Cambridge University Press
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Author and book information
Book Chapter
Pages
: 47-58
DOI:
10.1017/CBO9780511613357.004
SO-VID:
a959fcd7-2229-4e6f-8d8c-4b5fc2de9a9a
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Book chapters
pp. xxiii
Preface
pp. 1
Introduction
pp. 19
Some equations of interest and numerical approaches to solving them
pp. 47
Duality transformations in two-dimensional media
pp. 59
Translations and equivalent media
pp. 75
Some microstructure-independent exact relations
pp. 93
Exact relations for coupled equations
pp. 113
Assemblages of spheres, ellipsoids, and other neutral inclusions
pp. 143
Tricks for generating other exactly solvable microgeometries
pp. 159
Laminate materials
pp. 185
Approximations and asymptotic formulas
pp. 221
Wave propagation in the quasistatic limit
pp. 245
Reformulating the problem of finding effective tensors
pp. 271
Variational principles and inequalities
pp. 291
Series expansions for the fields and effective tensors
pp. 313
Correlation functions and how they enter series expansions†
pp. 341
Other perturbation solutions
pp. 355
The general theory of exact relations and links between effective tensors
pp. 369
Analytic properties
pp. 397
Y-tensors
pp. 413
Y-tensors and effective tensors in electrical circuits†
pp. 425
Bounds on the properties of composites
pp. 437
Classical variational principle bounds
pp. 457
Bounds from the Hashin-Shtrikman variational inequalities
pp. 499
Bounds using the compensated compactness or translation method
pp. 529
Choosing the translations and finding microgeometries that attain the bounds†
pp. 553
Bounds incorporating three-point correlation functions†
pp. 569
Bounds using the analytic method
pp. 603
Fractional linear transformations as a tool for generating bounds†
pp. 619
The field equation recursion method†
pp. 643
Properties of the G-closure and extremal families of composites
pp. 671
The bounding of effective moduli as a quasiconvexification problem
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