The theory of composites /

The theory of composites /

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Bibliographic Details
Author / Creator:	Milton, Graeme Walter, 1956- author.
Imprint:	Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM), [2023]
Description:	1 online resource (1 PDF (xl, 719 pages) :) illustrations.
Language:	English
Series:	Classics in applied mathematics ; 88.
Subject:	Composite materials. Differential equations, Partial. Homogenization (Differential equations) Composite materials Differential equations, Partial Homogenization (Differential equations)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/13565140

Hidden Bibliographic Details
Other authors / contributors:	Society for Industrial and Applied Mathematics, publisher.
ISBN:	9781611977486 1611977487
Notes:	Includes bibliographical references and indexes. Description based on title page of print version
Summary:	Composites have been studied for more than 150 years, and interest in their properties has been growing. The Theory of Composites is a classic volume, providing the foundations for understanding a broad range of composite properties. These properties can be explored either through the model geometries or through microstructure-independent bounds, obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties.
Other form:	Print version 9781611977479
Publisher's no.:	CL88 SIAM

Table of Contents:

Introduction
Some equations of interest and numerical approaches to solving them
Duality transformations in two-dimensional media
Translations and equivalent media
Some microstructure-independent exact relations
Exact relations for coupled equations
Assemblages of spheres, ellipsoids, and other neutral inclusions
Tricks for generating other exactly solvable microgeometries
Laminate materials
Approximations and asymptotic formulas
Wave propagation in the quasistatic limit
Reformulating the problem of finding effective tensors
Variational principles and inequalities
Series expansions for the fields and effective tensors
Correlation functions and how they enter series expansions
Other perturbation solutions
The general theory of exact relations and links between effective tensors
Analytic properties
Y-tensors
Y-tensors and effective tensors in electrical circuits
Bounds on the properties of composites
Classical variational principle bounds
Bounds from the Hashin-Shtrikman variational inequalities
Bounds using the compensated compactness or translation method
Choosing the translations and finding microgeometries that attain the bounds
Bounds incorporating three-point correlation functions
Bounds using the analytic method
Fractional linear transformations as a tool for generating bounds
The field equation recursion method
Properties of the G-closure and extremal families of composites
The bounding of effective moduli as a quasiconvexification problem.