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
