  The modeling of the elastic properties of granular or nanoscale systems
requires the foundations of the theory of elasticity to be revisited, as one
explores scales at which this theory may no longer hold. The only cases for
which a microscopic justification of elasticity exists are (nearly) uniformly
strained lattices. A microscopic theory of elasticity, as well as simulations,
reveal that standard continuum elasticity applies only at sufficiently large
scales (typically 100 particle diameters). Interestingly, force chains, which
have been observed in experiments on granular systems, and attributed to
non-elastic effects, are shown to exist in systems composed of harmonically
interacting constituents. The corresponding stress field, which is a continuum
mechanical (averaged) entity, exhibits no chain structures even at
near-microscopic resolutions, but it does reflect macroscopic anisotropy, when
present.
