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Progress in Nonlinear Differential Equations and Their Applications

Topics in the Mathematical Modelling of Composite Materials

Editors: Cherkaev, Andrej V., Kohn, R. (Eds.)

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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


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $139.00
price for USA in USD (gross)
  • ISBN 978-1-4612-2032-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $279.99
price for USA in USD
  • ISBN 978-0-8176-3662-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.99
price for USA in USD
  • ISBN 978-1-4612-7390-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in the Mathematical Modelling of Composite Materials
Editors
  • Andrej V. Cherkaev
  • R. Kohn
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
31
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-2032-9
DOI
10.1007/978-1-4612-2032-9
Hardcover ISBN
978-0-8176-3662-3
Softcover ISBN
978-1-4612-7390-5
Series ISSN
1421-1750
Edition Number
1
Number of Pages
XIV, 321
Topics