Topics in the Mathematical Modelling of Composite Materials: 31 (Progress in Nonlinear Differential Equations and Their Applications, 31) - Hardcover

Hardcover

ISBN 10: 0817636625 ISBN 13: 9780817636623

Publisher: Birkhäuser, 1997

Synopsis

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.

About this title

Review

"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

Synopsis

A collection of research papers dealing with the macroscopic behaviour of microscopically hetergenous materials. The papers have been previously published in French or Russian as "hidden literature". This volume provides English translations of these works.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• Language: English
• ISBN 10: 0817636625
• ISBN 13: 9780817636623
• Binding: Hardcover
• Number of pages: 335
• Editor: Cherkaev Andrej V., Kohn Robert