  Recent experimental results on the static or quasistatic response of granular
materials have been interpreted to suggest the inapplicability of the
traditional engineering approaches, which are based on elasto-plastic models
(which are elliptic in nature). Propagating (hyperbolic) or diffusive
(parabolic) models have been proposed to replace the `old' models. Since
several recent experiments were performed on small systems, one should not
really be surprised that (continuum) elasticity, a macroscopic theory, is not
directly applicable, and should be replaced by a grain-scale (``microscopic'')
description. Such a description concerns the interparticle forces, while a
macroscopic description is given in terms of the stress field. These
descriptions are related, but not equivalent, and the distinction is important
in interpreting the experimental results. There are indications that at least
some large scale properties of granular assemblies can be described by
elasticity, although not necessarily its isotropic version. The purely
repulsive interparticle forces (in non-cohesive materials) may lead to
modifications of the contact network upon the application of external forces,
which may strongly affect the anisotropy of the system. This effect is expected
to be small (in non-isostatic systems) for small applied forces and for
pre-stressed systems (in particular for disordered systems). Otherwise, it may
be accounted for using a nonlinear, incrementally elastic model, with
stress-history dependent elastic moduli. Although many features of the
experiments may be reproduced using models of frictionless particles, results
demonstrating the importance of accounting for friction are presented.
