New estimates of overall properties of heterogeneous solids

摘要

A complete formal similarity of the standard techniques for estimating overall elastic properties and phase averages of local mechanical and transformation stress and strain fields in heterogeneous materials is established for the self-consistent and Mori-Tanaka methods, and for Walpole's formulation of the Hashin-Shtrikman variational bounds. Regardless of the dissimilar and often heuristic assumptions that had motivated the original formulations, the only essential difference between these techniques had been the choice of the comparison medium where each phase was assumed to be embedded in the solution of the inclusion problem. Therefore, any number of related averaging methods can be developed from other choices made such that the resulting moduli predictions do not violate the bounds. Several new types of admissible comparison media are proposed and evaluated for composites reinforced by spherical particles or aligned fibers and also for porous media with spherical cavities. Many new estimates of overall moduli and local mechanical and transformation field averages can be obtained in this manner, for modeling and/or interpretation of a variety of experimental data in two or multiphase heterogeneous aggregates. A close agreement with the self-consistent results is found for one of the proposed choices.