Book contents
- Frontmatter
- Contents
- List of figures
- Preface
- 1 Introduction
- 2 Some equations of interest and numerical approaches to solving them
- 3 Duality transformations in two-dimensional media
- 4 Translations and equivalent media
- 5 Some microstructure-independent exact relations
- 6 Exact relations for coupled equations
- 7 Assemblages of spheres, ellipsoids, and other neutral inclusions
- 8 Tricks for generating other exactly solvable microgeometries
- 9 Laminate materials
- 10 Approximations and asymptotic formulas
- 11 Wave propagation in the quasistatic limit
- 12 Reformulating the problem of finding effective tensors
- 13 Variational principles and inequalities
- 14 Series expansions for the fields and effective tensors
- 15 Correlation functions and how they enter series expansions†
- 16 Other perturbation solutions
- 17 The general theory of exact relations and links between effective tensors
- 18 Analytic properties
- 19 Y-tensors
- 20 Y-tensors and effective tensors in electrical circuits†
- 21 Bounds on the properties of composites
- 22 Classical variational principle bounds
- 23 Bounds from the Hashin-Shtrikman variational inequalities
- 24 Bounds using the compensated compactness or translation method
- 25 Choosing the translations and finding microgeometries that attain the bounds†
- 26 Bounds incorporating three-point correlation functions†
- 27 Bounds using the analytic method
- 28 Fractional linear transformations as a tool for generating bounds†
- 29 The field equation recursion method†
- 30 Properties of the G-closure and extremal families of composites
- 31 The bounding of effective moduli as a quasiconvexification problem
- Author index
- Subject index
2 - Some equations of interest and numerical approaches to solving them
- Frontmatter
- Contents
- List of figures
- Preface
- 1 Introduction
- 2 Some equations of interest and numerical approaches to solving them
- 3 Duality transformations in two-dimensional media
- 4 Translations and equivalent media
- 5 Some microstructure-independent exact relations
- 6 Exact relations for coupled equations
- 7 Assemblages of spheres, ellipsoids, and other neutral inclusions
- 8 Tricks for generating other exactly solvable microgeometries
- 9 Laminate materials
- 10 Approximations and asymptotic formulas
- 11 Wave propagation in the quasistatic limit
- 12 Reformulating the problem of finding effective tensors
- 13 Variational principles and inequalities
- 14 Series expansions for the fields and effective tensors
- 15 Correlation functions and how they enter series expansions†
- 16 Other perturbation solutions
- 17 The general theory of exact relations and links between effective tensors
- 18 Analytic properties
- 19 Y-tensors
- 20 Y-tensors and effective tensors in electrical circuits†
- 21 Bounds on the properties of composites
- 22 Classical variational principle bounds
- 23 Bounds from the Hashin-Shtrikman variational inequalities
- 24 Bounds using the compensated compactness or translation method
- 25 Choosing the translations and finding microgeometries that attain the bounds†
- 26 Bounds incorporating three-point correlation functions†
- 27 Bounds using the analytic method
- 28 Fractional linear transformations as a tool for generating bounds†
- 29 The field equation recursion method†
- 30 Properties of the G-closure and extremal families of composites
- 31 The bounding of effective moduli as a quasiconvexification problem
- Author index
- Subject index
- Type
- Chapter
- Information
- The Theory of Composites , pp. 19 - 46Publisher: Cambridge University PressPrint publication year: 2002