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Topics in the Mathematical Modelling of Composite Materials

  • Book
  • © 1997

Overview

Editors:
  1. Andrej Cherkaev

    1. Department of Mathematics, University of Utah, Salt Lake City, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Robert Kohn

    1. Courant Mathematical Institute, New York University, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 31)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
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  2. On the Control of Coefficients in Partial Differential Equations

    • François Murat, Luc Tartar
    Pages 1-8

  3. Estimations of Homogenized Coefficients

    • Luc Tartar
    Pages 9-20

  4. H-Convergence

    • François Murat, Luc Tartar
    Pages 21-43

  5. A Strange Term Coming from Nowhere

    • Doina Cioranescu, François Murat
    Pages 45-93

  6. Design of Composite Plates of Extremal Rigidity

    • L. V. Gibiansky, A. V. Cherkaev
    Pages 95-137

  7. Calculus of Variations and Homogenization

    • François Murat, Luc Tartar
    Pages 139-173

  8. Effective Characteristics of Composite Materials and the Optimal Design of Structural Elements

    • K. A. Lurie, A. V. Cherkaev
    Pages 175-271

  9. Microstructures of Composites of Extremal Rigidity and Exact Bounds on the Associated Energy Density

    • L. V. Gibiansky, A. V. Cherkaev
    Pages 273-317

  10. Back Matter

    Pages 319-321
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Keywords

About this book

Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate­ rials. This activity brings together a number of related themes, including: ( 1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "com­ pensated compactness"; and (4) the identification of deep links between the analysis of microstructures and the multidimensional calculus of variations. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. As a result it has received attention and support from numerous scientific communities, including engineering, materials science, and physics as well as mathematics. There is by now an extensive literature in this area. But for various reasons certain fundamental papers were never properly published, circu­ lating instead as mimeographed notes or preprints. Other work appeared in poorly distributed conference proceedings volumes. Still other work was published in standard books or journals, but written in Russian or French. The net effect is a sort of "gap" in the literature, which has made the subject unnecessarily difficult for newcomers to penetrate.

Reviews

"Summarizes some of the fundamental results achieved and offers new perspectives in the mechanics of composite and micromechanics... Will become a classic in the two fields."

--Applied Mechanics Review

Editors and Affiliations

  • Department of Mathematics, University of Utah, Salt Lake City, USA

    Andrej Cherkaev

  • Courant Mathematical Institute, New York University, New York, USA

    Robert Kohn

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