We consider the mechanical behavior of particulate solids formed as aggregates of ultra-fine particles. For ultra-fine particles the particle size and the range of interactions of molecules (or atoms) are comparable. Thus the long-range interactions play an important role in the mechanics of such particle aggregates. Considering molecular (or atomic) interactions, expressions are derived for the inter-particle potential which account for particle deformations. These inter-particle potentials are used to obtain total potential of particle aggregates. The behavior is studied with emphasis upon the relationship between the particle interactions and the bulk behavior of aggregates. Using the total potential, expressions for stress tensor and elastic constants are derived. The elastic constants may be decomposed into a homogeneous term and a relaxation term.
