APPLICATION OF VARIATIONAL CONCEPTS TO SIZE EFFECTS IN ELASTIC HETEROGENEOUS BODIES

Heterogeneous materials that are not statistically uniform are considered. The basic assumptions and conditions underlying the concept of effective properties are reviewed. A general procedure for the experimental or numerical evaluation of the overall properties of the material when the concept of a representative volume does not apply or cannot be used is proposed and then applied to the elastic case as a first example. Three kinds of results are obtained: relationships between experimental results obtained on a large specimen and on an appropriate set of smaller ones, hierarchies between families of specimens of various sizes, absolute bounds for the two limiting cases where the size goes to zero, or to the representative volume when it exists. Possible applications and extensions are mentioned. © 1990.