Over the past several decades, we have witnessed a renaissance of
theoretical work on the macroscopic behavior of microscopically
heterogeneous materials. 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 "compensated
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, circulating 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. The
present, softcover reprint is designed to make this classic text
available to a wider audience.
"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
